6m(m-3)+20=8+3m(5-2m)

Solution for 6m(m-3)+20=8+3m(5-2m) equation:

6m(m-3)+20=8+3m(5-2m)

We move all terms to the left:

6m(m-3)+20-(8+3m(5-2m))=0

We add all the numbers together, and all the variables

6m(m-3)-(8+3m(-2m+5))+20=0

We multiply parentheses

6m^2-18m-(8+3m(-2m+5))+20=0


We calculate terms in parentheses: -(8+3m(-2m+5)), so:

8+3m(-2m+5)

determiningTheFunctionDomain
3m(-2m+5)+8

We multiply parentheses

-6m^2+15m+8

Back to the equation:

-(-6m^2+15m+8)


We get rid of parentheses

6m^2+6m^2-15m-18m-8+20=0

We add all the numbers together, and all the variables

12m^2-33m+12=0

a = 12; b = -33; c = +12;
Δ = b2-4ac
Δ = -332-4·12·12
Δ = 513
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:

$\sqrt{\Delta}=\sqrt{513}=\sqrt{9*57}=\sqrt{9}*\sqrt{57}=3\sqrt{57}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-33)-3\sqrt{57}}{2*12}=\frac{33-3\sqrt{57}}{24}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-33)+3\sqrt{57}}{2*12}=\frac{33+3\sqrt{57}}{24}
$