-16(x)^2+72(x)+55=0

Solution for -16(x)^2+72(x)+55=0 equation:

-16(x)^2+72(x)+55=0

a = -16; b = 72; c = +55;
Δ = b2-4ac
Δ = 722-4·(-16)·55
Δ = 8704
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:

$\sqrt{\Delta}=\sqrt{8704}=\sqrt{256*34}=\sqrt{256}*\sqrt{34}=16\sqrt{34}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(72)-16\sqrt{34}}{2*-16}=\frac{-72-16\sqrt{34}}{-32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(72)+16\sqrt{34}}{2*-16}=\frac{-72+16\sqrt{34}}{-32}
$