x=-16x^2+100

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

x=-16x^2+100

We move all terms to the left:

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

We get rid of parentheses

16x^2+x-100=0

a = 16; b = 1; c = -100;
Δ = b2-4ac
Δ = 12-4·16·(-100)
Δ = 6401
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-\sqrt{6401}}{2*16}=\frac{-1-\sqrt{6401}}{32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{6401}}{2*16}=\frac{-1+\sqrt{6401}}{32}
$