5m(9m-10)=0

Solution for 5m(9m-10)=0 equation:

5m(9m-10)=0

We multiply parentheses

45m^2-50m=0

a = 45; b = -50; c = 0;
Δ = b2-4ac
Δ = -502-4·45·0
Δ = 2500
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2500}=50$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-50)-50}{2*45}=\frac{0}{90}
=0
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-50)+50}{2*45}=\frac{100}{90}
=1+1/9
$