-2x^2+44x+8=0

Solution for -2x^2+44x+8=0 equation:

-2x^2+44x+8=0

a = -2; b = 44; c = +8;
Δ = b2-4ac
Δ = 442-4·(-2)·8
Δ = 2000
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:

$\sqrt{\Delta}=\sqrt{2000}=\sqrt{400*5}=\sqrt{400}*\sqrt{5}=20\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(44)-20\sqrt{5}}{2*-2}=\frac{-44-20\sqrt{5}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(44)+20\sqrt{5}}{2*-2}=\frac{-44+20\sqrt{5}}{-4}
$