X^2+5x-122=8x-2

Solution for X^2+5x-122=8x-2 equation:

X^2+5X-122=8X-2

We move all terms to the left:

X^2+5X-122-(8X-2)=0

We get rid of parentheses

X^2+5X-8X+2-122=0

We add all the numbers together, and all the variables

X^2-3X-120=0

a = 1; b = -3; c = -120;
Δ = b2-4ac
Δ = -32-4·1·(-120)
Δ = 489
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{-(-3)-\sqrt{489}}{2*1}=\frac{3-\sqrt{489}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{489}}{2*1}=\frac{3+\sqrt{489}}{2}
$