9x^2=30x+25=11

Solution for 9x^2=30x+25=11 equation:

9x^2=30x+25=11

We move all terms to the left:

9x^2-(30x+25)=0

We get rid of parentheses

9x^2-30x-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:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

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