0.5m(2m-3)-0.8=2.7

Solution for 0.5m(2m-3)-0.8=2.7 equation:

0.5m(2m-3)-0.8=2.7

We move all terms to the left:

0.5m(2m-3)-0.8-(2.7)=0

We add all the numbers together, and all the variables

0.5m(2m-3)-3.5=0

We multiply parentheses

0m^2+0m-3.5=0

We add all the numbers together, and all the variables

m^2+m-3.5=0

a = 1; b = 1; c = -3.5;
Δ = b2-4ac
Δ = 12-4·1·(-3.5)
Δ = 15
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{-(1)-\sqrt{15}}{2*1}=\frac{-1-\sqrt{15}}{2}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{15}}{2*1}=\frac{-1+\sqrt{15}}{2}
$