12x-2x^2=8

Solution for 12x-2x^2=8 equation:

12x-2x^2=8

We move all terms to the left:

12x-2x^2-(8)=0

a = -2; b = 12; c = -8;
Δ = b2-4ac
Δ = 122-4·(-2)·(-8)
Δ = 80
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:

$\sqrt{\Delta}=\sqrt{80}=\sqrt{16*5}=\sqrt{16}*\sqrt{5}=4\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-4\sqrt{5}}{2*-2}=\frac{-12-4\sqrt{5}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+4\sqrt{5}}{2*-2}=\frac{-12+4\sqrt{5}}{-4}
$