12m(m-2)=5m+2

Solution for 12m(m-2)=5m+2 equation:

12m(m-2)=5m+2

We move all terms to the left:

12m(m-2)-(5m+2)=0

We multiply parentheses

12m^2-24m-(5m+2)=0

We get rid of parentheses

12m^2-24m-5m-2=0

We add all the numbers together, and all the variables

12m^2-29m-2=0

a = 12; b = -29; c = -2;
Δ = b2-4ac
Δ = -292-4·12·(-2)
Δ = 937
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{-(-29)-\sqrt{937}}{2*12}=\frac{29-\sqrt{937}}{24}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-29)+\sqrt{937}}{2*12}=\frac{29+\sqrt{937}}{24}
$