2(x^2+20x-78)=0

Solution for 2(x^2+20x-78)=0 equation:

2(x^2+20x-78)=0

We multiply parentheses

2x^2+40x-156=0

a = 2; b = 40; c = -156;
Δ = b2-4ac
Δ = 402-4·2·(-156)
Δ = 2848
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:

$\sqrt{\Delta}=\sqrt{2848}=\sqrt{16*178}=\sqrt{16}*\sqrt{178}=4\sqrt{178}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(40)-4\sqrt{178}}{2*2}=\frac{-40-4\sqrt{178}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(40)+4\sqrt{178}}{2*2}=\frac{-40+4\sqrt{178}}{4}
$