8m(m-1)-17(3-m)=4-12(3-2m)

Solution for 8m(m-1)-17(3-m)=4-12(3-2m) equation:

8m(m-1)-17(3-m)=4-12(3-2m)

We move all terms to the left:

8m(m-1)-17(3-m)-(4-12(3-2m))=0

We add all the numbers together, and all the variables

8m(m-1)-17(-1m+3)-(4-12(-2m+3))=0

We multiply parentheses

8m^2-8m+17m-(4-12(-2m+3))-51=0


We calculate terms in parentheses: -(4-12(-2m+3)), so:

4-12(-2m+3)

determiningTheFunctionDomain
-12(-2m+3)+4

We multiply parentheses

24m-36+4

We add all the numbers together, and all the variables

24m-32

Back to the equation:

-(24m-32)


We add all the numbers together, and all the variables

8m^2+9m-(24m-32)-51=0

We get rid of parentheses

8m^2+9m-24m+32-51=0

We add all the numbers together, and all the variables

8m^2-15m-19=0

a = 8; b = -15; c = -19;
Δ = b2-4ac
Δ = -152-4·8·(-19)
Δ = 833
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:

$\sqrt{\Delta}=\sqrt{833}=\sqrt{49*17}=\sqrt{49}*\sqrt{17}=7\sqrt{17}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-7\sqrt{17}}{2*8}=\frac{15-7\sqrt{17}}{16}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+7\sqrt{17}}{2*8}=\frac{15+7\sqrt{17}}{16}
$