2x^2=12x+4

Solution for 2x^2=12x+4 equation:

2x^2=12x+4

We move all terms to the left:

2x^2-(12x+4)=0

We get rid of parentheses

2x^2-12x-4=0

a = 2; b = -12; c = -4;
Δ = b2-4ac
Δ = -122-4·2·(-4)
Δ = 176
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:

$\sqrt{\Delta}=\sqrt{176}=\sqrt{16*11}=\sqrt{16}*\sqrt{11}=4\sqrt{11}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-4\sqrt{11}}{2*2}=\frac{12-4\sqrt{11}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+4\sqrt{11}}{2*2}=\frac{12+4\sqrt{11}}{4}
$