Solve the equtaion?

Question

Solve the equation

6x² + 17x - 39 = 0

I think you may have to use the formula for quadratic equations but i'm not 100% sure

Thankyou

Answer 1

The easiest way is to use the quadratic formula, you're right!

The solutions of a quadratic equation
ax² + bx + c = 0
are
x = [ - b ± √(b² - 4ac)] / 2a

For 6x² + 17x - 39 = 0,
a = 6, b = 17 and c = -39, so

x = [ - 17 ± √(17² - 4·6·(-39))] / 2·6

x = [ - 17 ± √(289 + 936)] / 12

x = [ - 17 ± √1225] / 12

x = [- 17 ± 35] / 12

So the two solutions are
=> x = [- 17 + 35] / 12 = 18/12 = 3/2
and
=> x = [- 17 - 35] / 12 = -52/12 = -13/3

__________

If you didn't use the quadratic formula, you could also factor
6x² + 17x - 39 = 0
(2x - 3)(3x + 13) = 0
=> x = 3/2, x = -13/3
___________

Hope this helps.

Answer 2

A quick check is the discriminant b^2-4ac
= 289 +24*39 which comes to 1225 which is 35^2 so it will factorise easily

x = -b+-sqr(discriminant)/2a
x = (-17 +-35)/12
x = 1 1/2 or x = -4 1/3

( 2x-3)( 3x+13)

Answer 3

you may use this formula of quadratic equation for finding the unknown values in this case.

given eq. : 6x² + 17x - 39 = 0

quadratic eq.:

ax² + bx + c = 0

x = [ - b ± √(b² - 4ac)] / 2a

there are two answers to this equation, because
there is ± with respect to the root of the equations.
one answer is:

x = 1.5

the other is:

x = - 4.3333333

ok.

Answer 4

The quadratic equation formula will work. If you have a negative c coefficient and a value of a not equal to 1 that is usually a good sign of it needing the quadratic formula.

Answer 5

6x^2+17x -39 = 0
6^2 -9x +26x -39 =0
3x(2x - 3) +13(2x - 3) =0
(2x - 3)(3x + 13) =0
2x -3 =0 or 3x +13 =0
2x = 3 or 3x = -13
x =3/2 or x = -13/3

Answer 6

6x² + 17x - 39 = 0
x = [-17 +- SQRT(17² - 4(6)(-39)] / (2)(6)
x = [-17 +- 35] / 12
x = 1 1/2, -4 1/3

Answer 7

6x²+17x-39=0
(2x-3)(3x+13)=0

therefore x=3/2 or -13/3

Hope that helps

Answer 8

6x² + 17x - 39 = 0

Solving with the quadractic equation
x = (-b +- √(b² - 4ac))/2a

x = (-17 +- √(289 + 936))/12

x = (-17 +- √(1225))/12

x = (-17 +- 35)/12

x = -0.433, x = 1.5
.

Answer 9

It factors to
(2x - 3)(3x + 13) = 0

================
quadratic formula is

(1 / 2a)(-b +- sqrt (b^2 - 4ac))

in your case...
a = 6
b = 17
c = -39

Starting from the inside...
b^2 - 4ac
= (17)^2 - 4(6)(-39)
= 289 + 936
= 1225

square root of that is...
sqrt 1225 = 35

So, now you have
- b +- 35
= -17 +- 35
= 18 and -52

AND
(1 / 2a) = 1 / 2*6 = 1/12

So....
(1/12)(18) AND (1/12)(-52)

or...
18/12 AND -52/12

simplified...
3/2 AND -13/3

Answer 10

6x2 + 17x - 39 = 0
6x2 + 26x - 9x - 39 = 0
2x(3x + 13) - 3( 3x + 13) = 0
therefore, (2x - 3) * (3x + 13) = 0
therfore, 2x -3 = 0 OR 3x + 13 =0
therefore, x = 3/2 OR x = -13/3