Question

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

Please show all your work! (30 points)

Answer 1

the quadratic formula can be aplied as follows:
for
`ax^2+bx+c=0`,
`x=(-b \pm √(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=(-(-7) \pm √((-7)^2-4(2)(-6)))/(2(2))`

`x=(7 \pm √(49+48))/(4)`

`x=(7 \pm √(97))/(4)`

so
`x=(7 + √(97))/(4)` or
`x=(7 - √(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