6(m^2-8m+15)=0

Solution for 6(m^2-8m+15)=0 equation:

6(m^2-8m+15)=0

We multiply parentheses

6m^2-48m+90=0

a = 6; b = -48; c = +90;
Δ = b2-4ac
Δ = -482-4·6·90
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-48)-12}{2*6}=\frac{36}{12}
=3
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-48)+12}{2*6}=\frac{60}{12}
=5
$