25x^2-90x=81=0

Solution for 25x^2-90x=81=0 equation:

25x^2-90x=81=0

We move all terms to the left:

25x^2-90x-(81)=0

a = 25; b = -90; c = -81;
Δ = b2-4ac
Δ = -902-4·25·(-81)
Δ = 16200
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:

$\sqrt{\Delta}=\sqrt{16200}=\sqrt{8100*2}=\sqrt{8100}*\sqrt{2}=90\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-90)-90\sqrt{2}}{2*25}=\frac{90-90\sqrt{2}}{50}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-90)+90\sqrt{2}}{2*25}=\frac{90+90\sqrt{2}}{50}
$