Question

Use the quadratic formula to solve, 2x^2=7x+6 Leave your answer in simplified radical form.

Answer 1

The quadratic formula can be aplied as follows:
for $ax^2+bx+c=0$, $x=\frac{-b \pm \sqrt{b^2-4ac}}{2a}$


given $2x^2=7x+6$
we need to get it into $ax^2+bx+c=0$ form

minus (7x+6) from both sides
$2x^2-7x-6=0$
now, a=2, b=-7 c=-6
subsitute
$x=\frac{-(-7) \pm \sqrt{(-7)^2-4(2)(-6)}}{2(2)}$
$x=\frac{7 \pm \sqrt{49+48}}{4}$
$x=\frac{7 \pm \sqrt{97}}{4}$

so $x=\frac{7 + \sqrt{97}}{4}$ or $x=\frac{7 - \sqrt{97}}{4}$

Answer 2

2x² = 7x + 6

Subtract both terms so that we can get 0 on one side. 

2x² - 7x - 6 = 0

Find what factors of - 12 (2 * - 6) add up to be - 7. It's - 4 and - 3. 

2x² - 4x - 3x - 6 = 0
2x(x - 2) - 3(x - 2) = 0
(x - 2)(2x - 3) = 0

Now set each equal to 0.

x - 2 = 0
x = 2

2x - 3 = 0
2x = 3
x = 3/2

x = 3/2, 2