4=-2x^2+12x

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

4=-2x^2+12x

We move all terms to the left:

4-(-2x^2+12x)=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 = 112
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:

$\sqrt{\Delta}=\sqrt{112}=\sqrt{16*7}=\sqrt{16}*\sqrt{7}=4\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-4\sqrt{7}}{2*2}=\frac{12-4\sqrt{7}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+4\sqrt{7}}{2*2}=\frac{12+4\sqrt{7}}{4}
$