X^2-2x=4x+82

Solution for X^2-2x=4x+82 equation:

X^2-2X=4X+82

We move all terms to the left:

X^2-2X-(4X+82)=0

We get rid of parentheses

X^2-2X-4X-82=0

We add all the numbers together, and all the variables

X^2-6X-82=0

a = 1; b = -6; c = -82;
Δ = b2-4ac
Δ = -62-4·1·(-82)
Δ = 364
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:

$\sqrt{\Delta}=\sqrt{364}=\sqrt{4*91}=\sqrt{4}*\sqrt{91}=2\sqrt{91}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{91}}{2*1}=\frac{6-2\sqrt{91}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{91}}{2*1}=\frac{6+2\sqrt{91}}{2}
$