2x^2+8x-52=0

Solution for 2x^2+8x-52=0 equation:

2x^2+8x-52=0

a = 2; b = 8; c = -52;
Δ = b2-4ac
Δ = 82-4·2·(-52)
Δ = 480
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:

$\sqrt{\Delta}=\sqrt{480}=\sqrt{16*30}=\sqrt{16}*\sqrt{30}=4\sqrt{30}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-4\sqrt{30}}{2*2}=\frac{-8-4\sqrt{30}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+4\sqrt{30}}{2*2}=\frac{-8+4\sqrt{30}}{4}
$