How do you solve 3x^2-5x+4=0 using the quadratic formula to find the exact solutions?

Question

How do you solve 3x^2-5x+4=0 using the quadratic formula to find the exact solutions?

I know the answer is 5/6 +or- √23/6 i

I just really wanna figure out how to get that...

so far I have this:
X=5+-√-5^2-4(3)(4) / 2(3)

x=5=-√25-48 / 6

Any ideas? Im horrible at algebra.

Answer 1

To solve an equation in the for

ax^2 + bx + c = 0, for some real numbers a, b, and c,

The quadratic formula goes as follows:

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

The "+/-" symbol means "plus or minus". In the case of
3x^2 - 5x + 4 = 0
a = 3, b = -5 and c = 4. Plug into the formula and solve.

x = [ -(-5) +/- sqrt( (-5)^2 - 4(3)(4) ) ] / (2(3))

x = [5 +/- sqrt(25 - 48)] / (6)

x = [5 +/- sqrt(-23)] / 6

Putting each term over 6, we have

x = (5/6) +/- sqrt(-23)/6

It's worth noting that whenever we have the square root of a negative number, we will get a complex answer. Note that
sqrt(-23) is the same as sqrt(-1 * 23) = sqrt(-1)sqrt(23). Since sqrt(-1) = i, then sqrt(-23) = sqrt(23)i. For that reason, we have

x = (5/6) +/- (1/6) sqrt(23)i

Giving us the two answers of

x = {(5/6) + (1/6) sqrt(23)i , (5/6) - (1/6) sqrt(23)i }

Answer 2

Step 1: Memorize the Baskara's formula:
(-b +/- sqrt delta) over 2a

3x²-5x+4=0
Delta = -5² - 4.3.4
Delta = 25 -48
delta = -23

x =[ -(-5) +/- √-23] : 2*3
x' = [5 +/- √-23] : 6
x' = 5/6 + √-23/6
x" = 5/6 - √-23/6
Attention: -√23 is not equal √-23.
><

Answer 3

Instead of writing the square root, I have put the b^2 - 4ac to the power of 1/2, because it is the same thing. 3x^2 + 5x + 1 = 0 x = (-b + or - (b^2 - 4ac)^(1/2)) / 2a x = (-5 + or - (25 - 12)^(1/2)) / 6 x = (-5 +or- 13^(1/2))/6 x = -0.23 or x = -1.43

Answer 4

=[-5±√5^2-4(3)(4)]/ 2(3)

= [-5±√25-48]/ 6 Which you have, so your next step is to subtract inside the radical

=[-5±√-23]/6 you cant reduce the radical any more, and you cant reduce the fraction so your answer must be :
=[-5± 23i]/ 6

Answer 5

Since √[25-48] is the square root of a negative number, this equation does not have a numerical solution with real numbers. √[25-48] = 4.786i, and the solution is .833 ± .799i