-25x^2+100x=90

Solution for -25x^2+100x=90 equation:

-25x^2+100x=90

We move all terms to the left:

-25x^2+100x-(90)=0

a = -25; b = 100; c = -90;
Δ = b2-4ac
Δ = 1002-4·(-25)·(-90)
Δ = 1000
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:

$\sqrt{\Delta}=\sqrt{1000}=\sqrt{100*10}=\sqrt{100}*\sqrt{10}=10\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(100)-10\sqrt{10}}{2*-25}=\frac{-100-10\sqrt{10}}{-50}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(100)+10\sqrt{10}}{2*-25}=\frac{-100+10\sqrt{10}}{-50}
$