X^2-x-12=8x-2

Solution for X^2-x-12=8x-2 equation:

X^2-X-12=8X-2

We move all terms to the left:

X^2-X-12-(8X-2)=0

We add all the numbers together, and all the variables

X^2-1X-(8X-2)-12=0

We get rid of parentheses

X^2-1X-8X+2-12=0

We add all the numbers together, and all the variables

X^2-9X-10=0

a = 1; b = -9; c = -10;
Δ = b2-4ac
Δ = -92-4·1·(-10)
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-11}{2*1}=\frac{-2}{2}
=-1
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+11}{2*1}=\frac{20}{2}
=10
$