What is x if: 3x^2=2x+5?

Answer 1

Rearrange:

3x² - 2x - 5 = 0

Factor:

(3x - 5)(x + 1) = 0

x = 5/3 or x = -1

Answer 2

3x^2 = 2x+5

Get everything on one side. We want a formula that looks like ax^2 + bx + c = 0.
Subtract the 2x from both sides.
3x^2 = 2x(-2x)+5
=
(3x^2) - 2x = 5
Note that the 2x is canceled on the right side and we are left with just the five.
Subtract 5 from both sides.
(3x^2) - 2x (-5) = 5-5
=
(3x^2) - 2x - 5 = 0
Finally we have what we need to solve. We can use one of two methods: Factor or the Quadratic Formula.

With factoring, we must find the roots of the quadratic equation 3x^2 - 2x - 5 = 0. We must do the inverse of FOILing.
What when multiplied will equal 3x^2? We need an x*x, but what are the cofactors? Most likely 1 and 3.

Thus far, we have
(3x )(x )
What, pair of numbers when added together will equal -2x? -5 and 3x? Additionally, what two numbers when multiplied equal -5? -5 and 1?
Combining all this data, we factor our problem into
(3x - 5)(x + 1)
We can check by FOILing this. FOIL stands for FIRST, OUTER, INNER, LAST. We multiply these numbers.
FIRST: 3x and x = 3x^2
OUTER: 3x and 1 = 3x
INNER: -5 and x = -5x
LAST : -5 and 1 = -5
Combine it all into one statement:
3x^2 + 3x - 5x - 5
Combine like terms (3x and -5x = -2x)
3x^2 - 2x - 5 = 0
We have factored correctly. To find possible solutions, take each half and set it equal to zero and solve for x:

3x - 5 = 0
Add five to each side.
3x = 5
Divide each side by 3.
3x = 5
-- --
3 3

3 cancels out,
x = 5/3

Now the other one.

x + 1 = 0
- 1 -1
x = -1

So x = 5/3 and -1 in this problem.


As an alternative, you can use the quadratic formula, which is much easier.

The quadratic formula is this:

x = -b +/- sqrt(b^2 - 4ac)
-----------------------
2a

Plugin:

x = 2 +/- sqrt(-2^2 -4(3)(-5) = 2 +/- sqrt(4+60) = 2 +/- 8
-------------------------------------------------------
2*3

So

x = 2 +/- 8
--------
6
x = 10/6 or -6/6
x = 5/3 or -1

Hope you got that all okay.

Answer 3

3x^2 - 2x -5 = 0
( 3x - 5 )( x + 1 ) = 0
x = 5/3 or -1

Answer 4

set the equation equal to 0
3x^2-2x-5=0
then factor
(3x-5)(x+1)
Then find the zeroes of the equations
x=5/3 and x= -1

Answer 5

3x^2 - 2X - 5 = 0
x = -1 and x = 1 2/3

Answer 6

3x^2=2x+5
3x^2-2x-5=0
(x+1)(3x-5) = 0


x = -1 or 5/3

Answer 7

3x ² - 2x - 5 = 0
x = [ 2 ± √(4 + 60) ] / 6
x = [ 2 ± 8 ] / 6
x = 10 / 6 , x = - 6 / 6
x = 5 / 3 , x = - 1

OR

(3x - 5) (x + 1) = 0
x = 5 / 3 , x = - 1

Answer 8

3x^2-2x-5=0
(3x-5)(x+1)=0
3x=5 and x=-1
x= 5/3; x= -1

Answer 9

3x^2=2x+5
or 3x^2 - 2x - 5 = 0
or 3x^2 + 3x - 5x - 5 = 0

the rest should be simple =)

Answer 10

Use the quadratic equation:

3x^2 = 2x + 5

Rearrange:

3x^2 - 2x - 5 = 0

Quadratic equation:
x = [-b +/- SQRT(b^2 - 4*a*c)]/2*a
ax^2 + bx + c = 0

in your equation:
a = 3
b = -2
c = -5

x = [2 +/- SQRT(2^2 - 4*3*-5)] / 2*3
x = [2 +/- SQRT(4 + 60)] / 6
x = [2 +/- 8] / 6
x = 10/6, -6/6

x = 5/3, -1