2x^2-56x-32=0

Solution for 2x^2-56x-32=0 equation:

2x^2-56x-32=0

a = 2; b = -56; c = -32;
Δ = b2-4ac
Δ = -562-4·2·(-32)
Δ = 3392
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:

$\sqrt{\Delta}=\sqrt{3392}=\sqrt{64*53}=\sqrt{64}*\sqrt{53}=8\sqrt{53}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-56)-8\sqrt{53}}{2*2}=\frac{56-8\sqrt{53}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-56)+8\sqrt{53}}{2*2}=\frac{56+8\sqrt{53}}{4}
$