-2/3m=m-12

Solution for -2/3m=m-12 equation:

-2/3m=m-12

We move all terms to the left:

-2/3m-(m-12)=0


Domain of the equation: 3m!=0

m!=0/3

m!=0

m∈R


We get rid of parentheses

-2/3m-m+12=0

We multiply all the terms by the denominator


-m*3m+12*3m-2=0

Wy multiply elements

-3m^2+36m-2=0

a = -3; b = 36; c = -2;
Δ = b2-4ac
Δ = 362-4·(-3)·(-2)
Δ = 1272
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:

$\sqrt{\Delta}=\sqrt{1272}=\sqrt{4*318}=\sqrt{4}*\sqrt{318}=2\sqrt{318}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(36)-2\sqrt{318}}{2*-3}=\frac{-36-2\sqrt{318}}{-6}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(36)+2\sqrt{318}}{2*-3}=\frac{-36+2\sqrt{318}}{-6}
$