-16x^2+100x+72=100

Solution for -16x^2+100x+72=100 equation:

-16x^2+100x+72=100

We move all terms to the left:

-16x^2+100x+72-(100)=0

We add all the numbers together, and all the variables

-16x^2+100x-28=0

a = -16; b = 100; c = -28;
Δ = b2-4ac
Δ = 1002-4·(-16)·(-28)
Δ = 8208
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:

$\sqrt{\Delta}=\sqrt{8208}=\sqrt{144*57}=\sqrt{144}*\sqrt{57}=12\sqrt{57}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(100)-12\sqrt{57}}{2*-16}=\frac{-100-12\sqrt{57}}{-32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(100)+12\sqrt{57}}{2*-16}=\frac{-100+12\sqrt{57}}{-32}
$