4m(m+2)-2(m^2-1)=5+3m

Solution for 4m(m+2)-2(m^2-1)=5+3m equation:

4m(m+2)-2(m^2-1)=5+3m

We move all terms to the left:

4m(m+2)-2(m^2-1)-(5+3m)=0

We add all the numbers together, and all the variables

4m(m+2)-2(m^2-1)-(3m+5)=0

We multiply parentheses

4m^2-2m^2+8m-(3m+5)+2=0

We get rid of parentheses

4m^2-2m^2+8m-3m-5+2=0

We add all the numbers together, and all the variables

2m^2+5m-3=0

a = 2; b = 5; c = -3;
Δ = b2-4ac
Δ = 52-4·2·(-3)
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-7}{2*2}=\frac{-12}{4}
=-3
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+7}{2*2}=\frac{2}{4}
=1/2
$