5m(5m+6)=9

Solution for 5m(5m+6)=9 equation:

5m(5m+6)=9

We move all terms to the left:

5m(5m+6)-(9)=0

We multiply parentheses

25m^2+30m-9=0

a = 25; b = 30; c = -9;
Δ = b2-4ac
Δ = 302-4·25·(-9)
Δ = 1800
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1800}=\sqrt{900*2}=\sqrt{900}*\sqrt{2}=30\sqrt{2}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-30\sqrt{2}}{2*25}=\frac{-30-30\sqrt{2}}{50}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+30\sqrt{2}}{2*25}=\frac{-30+30\sqrt{2}}{50}
$