8=2x^2+x-6

Solution for 8=2x^2+x-6 equation:

8=2x^2+x-6

We move all terms to the left:

8-(2x^2+x-6)=0

We get rid of parentheses

-2x^2-x+6+8=0

We add all the numbers together, and all the variables

-2x^2-1x+14=0

a = -2; b = -1; c = +14;
Δ = b2-4ac
Δ = -12-4·(-2)·14
Δ = 113
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-\sqrt{113}}{2*-2}=\frac{1-\sqrt{113}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{113}}{2*-2}=\frac{1+\sqrt{113}}{-4}
$