5m2=25m+120

Solution for 5m2=25m+120 equation:

5m^2=25m+120

We move all terms to the left:

5m^2-(25m+120)=0

We get rid of parentheses

5m^2-25m-120=0

a = 5; b = -25; c = -120;
Δ = b2-4ac
Δ = -252-4·5·(-120)
Δ = 3025
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3025}=55$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-25)-55}{2*5}=\frac{-30}{10}
=-3
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-25)+55}{2*5}=\frac{80}{10}
=8
$