100=72x-3x^2

Solution for 100=72x-3x^2 equation:

100=72x-3x^2

We move all terms to the left:

100-(72x-3x^2)=0

We get rid of parentheses

3x^2-72x+100=0

a = 3; b = -72; c = +100;
Δ = b2-4ac
Δ = -722-4·3·100
Δ = 3984
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:

$\sqrt{\Delta}=\sqrt{3984}=\sqrt{16*249}=\sqrt{16}*\sqrt{249}=4\sqrt{249}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-72)-4\sqrt{249}}{2*3}=\frac{72-4\sqrt{249}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-72)+4\sqrt{249}}{2*3}=\frac{72+4\sqrt{249}}{6}
$