X^2-4x-2=9x-8

Solution for X^2-4x-2=9x-8 equation:

X^2-4X-2=9X-8

We move all terms to the left:

X^2-4X-2-(9X-8)=0

We get rid of parentheses

X^2-4X-9X+8-2=0

We add all the numbers together, and all the variables

X^2-13X+6=0

a = 1; b = -13; c = +6;
Δ = b2-4ac
Δ = -132-4·1·6
Δ = 145
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{-(-13)-\sqrt{145}}{2*1}=\frac{13-\sqrt{145}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+\sqrt{145}}{2*1}=\frac{13+\sqrt{145}}{2}
$