-2x^2-8x+26=4

Solution for -2x^2-8x+26=4 equation:

-2x^2-8x+26=4

We move all terms to the left:

-2x^2-8x+26-(4)=0

We add all the numbers together, and all the variables

-2x^2-8x+22=0

a = -2; b = -8; c = +22;
Δ = b2-4ac
Δ = -82-4·(-2)·22
Δ = 240
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:

$\sqrt{\Delta}=\sqrt{240}=\sqrt{16*15}=\sqrt{16}*\sqrt{15}=4\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-4\sqrt{15}}{2*-2}=\frac{8-4\sqrt{15}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+4\sqrt{15}}{2*-2}=\frac{8+4\sqrt{15}}{-4}
$