26-2x^2=12x

Solution for 26-2x^2=12x equation:

26-2x^2=12x

We move all terms to the left:

26-2x^2-(12x)=0

a = -2; b = -12; c = +26;
Δ = b2-4ac
Δ = -122-4·(-2)·26
Δ = 352
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:

$\sqrt{\Delta}=\sqrt{352}=\sqrt{16*22}=\sqrt{16}*\sqrt{22}=4\sqrt{22}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-4\sqrt{22}}{2*-2}=\frac{12-4\sqrt{22}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+4\sqrt{22}}{2*-2}=\frac{12+4\sqrt{22}}{-4}
$