8x^2+56x+52=0

Solution for 8x^2+56x+52=0 equation:

8x^2+56x+52=0

a = 8; b = 56; c = +52;
Δ = b2-4ac
Δ = 562-4·8·52
Δ = 1472
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:

$\sqrt{\Delta}=\sqrt{1472}=\sqrt{64*23}=\sqrt{64}*\sqrt{23}=8\sqrt{23}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(56)-8\sqrt{23}}{2*8}=\frac{-56-8\sqrt{23}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(56)+8\sqrt{23}}{2*8}=\frac{-56+8\sqrt{23}}{16}
$