-16x^2+72x+52=0

Solution for -16x^2+72x+52=0 equation:

-16x^2+72x+52=0

a = -16; b = 72; c = +52;
Δ = b2-4ac
Δ = 722-4·(-16)·52
Δ = 8512
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:

$\sqrt{\Delta}=\sqrt{8512}=\sqrt{64*133}=\sqrt{64}*\sqrt{133}=8\sqrt{133}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(72)-8\sqrt{133}}{2*-16}=\frac{-72-8\sqrt{133}}{-32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(72)+8\sqrt{133}}{2*-16}=\frac{-72+8\sqrt{133}}{-32}
$