m.4(m+2.5)=7.5

Solution for m.4(m+2.5)=7.5 equation:

m.4(m+2.5)=7.5

We move all terms to the left:

m.4(m+2.5)-(7.5)=0

We add all the numbers together, and all the variables

m.4(m+2.5)-7.5=0

We multiply parentheses

m^2+2.5m-7.5=0

a = 1; b = 2.5; c = -7.5;
Δ = b2-4ac
Δ = 2.52-4·1·(-7.5)
Δ = 36.25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2.5)-\sqrt{36.25}}{2*1}=\frac{-2.5-\sqrt{36.25}}{2}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2.5)+\sqrt{36.25}}{2*1}=\frac{-2.5+\sqrt{36.25}}{2}
$