3/2m+5=3m-10

Solution for 3/2m+5=3m-10 equation:

3/2m+5=3m-10

We move all terms to the left:

3/2m+5-(3m-10)=0


Domain of the equation: 2m!=0

m!=0/2

m!=0

m∈R


We get rid of parentheses

3/2m-3m+10+5=0

We multiply all the terms by the denominator


-3m*2m+10*2m+5*2m+3=0

Wy multiply elements

-6m^2+20m+10m+3=0

We add all the numbers together, and all the variables

-6m^2+30m+3=0

a = -6; b = 30; c = +3;
Δ = b2-4ac
Δ = 302-4·(-6)·3
Δ = 972
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:

$\sqrt{\Delta}=\sqrt{972}=\sqrt{324*3}=\sqrt{324}*\sqrt{3}=18\sqrt{3}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-18\sqrt{3}}{2*-6}=\frac{-30-18\sqrt{3}}{-12}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+18\sqrt{3}}{2*-6}=\frac{-30+18\sqrt{3}}{-12}
$