X^2=12x-2

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

X^2=12X-2

We move all terms to the left:

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

We get rid of parentheses

X^2-12X+2=0

a = 1; b = -12; c = +2;
Δ = b2-4ac
Δ = -122-4·1·2
Δ = 136
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:

$\sqrt{\Delta}=\sqrt{136}=\sqrt{4*34}=\sqrt{4}*\sqrt{34}=2\sqrt{34}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-2\sqrt{34}}{2*1}=\frac{12-2\sqrt{34}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+2\sqrt{34}}{2*1}=\frac{12+2\sqrt{34}}{2}
$