-9u^2=30u-25

Solution for -9u^2=30u-25 equation:

-9u^2=30u-25

We move all terms to the left:

-9u^2-(30u-25)=0

We get rid of parentheses

-9u^2-30u+25=0

a = -9; b = -30; c = +25;
Δ = b2-4ac
Δ = -302-4·(-9)·25
Δ = 1800
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:

$\sqrt{\Delta}=\sqrt{1800}=\sqrt{900*2}=\sqrt{900}*\sqrt{2}=30\sqrt{2}$
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-30\sqrt{2}}{2*-9}=\frac{30-30\sqrt{2}}{-18}
$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+30\sqrt{2}}{2*-9}=\frac{30+30\sqrt{2}}{-18}
$