612=-16x^2+200x

Solution for 612=-16x^2+200x equation:

612=-16x^2+200x

We move all terms to the left:

612-(-16x^2+200x)=0

We get rid of parentheses

16x^2-200x+612=0

a = 16; b = -200; c = +612;
Δ = b2-4ac
Δ = -2002-4·16·612
Δ = 832
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:

$\sqrt{\Delta}=\sqrt{832}=\sqrt{64*13}=\sqrt{64}*\sqrt{13}=8\sqrt{13}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-200)-8\sqrt{13}}{2*16}=\frac{200-8\sqrt{13}}{32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-200)+8\sqrt{13}}{2*16}=\frac{200+8\sqrt{13}}{32}
$