/2m-31=-9m+24

Solution for /2m-31=-9m+24 equation:

/2m-31=-9m+24

We move all terms to the left:

/2m-31-(-9m+24)=0


Domain of the equation: 2m!=0

m!=0/2

m!=0

m∈R


We get rid of parentheses

/2m+9m-24-31=0

We multiply all the terms by the denominator


9m*2m-24*2m-31*2m+=0

We add all the numbers together, and all the variables

9m*2m-24*2m-31*2m=0

Wy multiply elements

18m^2-48m-62m=0

We add all the numbers together, and all the variables

18m^2-110m=0

a = 18; b = -110; c = 0;
Δ = b2-4ac
Δ = -1102-4·18·0
Δ = 12100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{12100}=110$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-110)-110}{2*18}=\frac{0}{36}
=0
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-110)+110}{2*18}=\frac{220}{36}
=6+1/9
$