4(m-12)=10m-6m(m-8)

Solution for 4(m-12)=10m-6m(m-8) equation:

4(m-12)=10m-6m(m-8)

We move all terms to the left:

4(m-12)-(10m-6m(m-8))=0

We multiply parentheses

4m-(10m-6m(m-8))-48=0


We calculate terms in parentheses: -(10m-6m(m-8)), so:

10m-6m(m-8)

We multiply parentheses

-6m^2+10m+48m

We add all the numbers together, and all the variables

-6m^2+58m

Back to the equation:

-(-6m^2+58m)


We get rid of parentheses

6m^2-58m+4m-48=0

We add all the numbers together, and all the variables

6m^2-54m-48=0

a = 6; b = -54; c = -48;
Δ = b2-4ac
Δ = -542-4·6·(-48)
Δ = 4068
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{4068}=\sqrt{36*113}=\sqrt{36}*\sqrt{113}=6\sqrt{113}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-54)-6\sqrt{113}}{2*6}=\frac{54-6\sqrt{113}}{12}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-54)+6\sqrt{113}}{2*6}=\frac{54+6\sqrt{113}}{12}
$