9u^2=90u-25

Solution for 9u^2=90u-25 equation:

9u^2=90u-25

We move all terms to the left:

9u^2-(90u-25)=0

We get rid of parentheses

9u^2-90u+25=0

a = 9; b = -90; c = +25;
Δ = b2-4ac
Δ = -902-4·9·25
Δ = 7200
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{7200}=\sqrt{3600*2}=\sqrt{3600}*\sqrt{2}=60\sqrt{2}$
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-90)-60\sqrt{2}}{2*9}=\frac{90-60\sqrt{2}}{18}
$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-90)+60\sqrt{2}}{2*9}=\frac{90+60\sqrt{2}}{18}
$