X^2-14x-18=8x-2

Solution for X^2-14x-18=8x-2 equation:

X^2-14X-18=8X-2

We move all terms to the left:

X^2-14X-18-(8X-2)=0

We get rid of parentheses

X^2-14X-8X+2-18=0

We add all the numbers together, and all the variables

X^2-22X-16=0

a = 1; b = -22; c = -16;
Δ = b2-4ac
Δ = -222-4·1·(-16)
Δ = 548
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{548}=\sqrt{4*137}=\sqrt{4}*\sqrt{137}=2\sqrt{137}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-22)-2\sqrt{137}}{2*1}=\frac{22-2\sqrt{137}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-22)+2\sqrt{137}}{2*1}=\frac{22+2\sqrt{137}}{2}
$