15+90x-16x^2=100

Solution for 15+90x-16x^2=100 equation:

15+90x-16x^2=100

We move all terms to the left:

15+90x-16x^2-(100)=0

We add all the numbers together, and all the variables

-16x^2+90x-85=0

a = -16; b = 90; c = -85;
Δ = b2-4ac
Δ = 902-4·(-16)·(-85)
Δ = 2660
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:

$\sqrt{\Delta}=\sqrt{2660}=\sqrt{4*665}=\sqrt{4}*\sqrt{665}=2\sqrt{665}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(90)-2\sqrt{665}}{2*-16}=\frac{-90-2\sqrt{665}}{-32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(90)+2\sqrt{665}}{2*-16}=\frac{-90+2\sqrt{665}}{-32}
$