2/3m+5=2m-1

Solution for 2/3m+5=2m-1 equation:

2/3m+5=2m-1

We move all terms to the left:

2/3m+5-(2m-1)=0


Domain of the equation: 3m!=0

m!=0/3

m!=0

m∈R


We get rid of parentheses

2/3m-2m+1+5=0

We multiply all the terms by the denominator


-2m*3m+1*3m+5*3m+2=0

Wy multiply elements

-6m^2+3m+15m+2=0

We add all the numbers together, and all the variables

-6m^2+18m+2=0

a = -6; b = 18; c = +2;
Δ = b2-4ac
Δ = 182-4·(-6)·2
Δ = 372
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:

$\sqrt{\Delta}=\sqrt{372}=\sqrt{4*93}=\sqrt{4}*\sqrt{93}=2\sqrt{93}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-2\sqrt{93}}{2*-6}=\frac{-18-2\sqrt{93}}{-12}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+2\sqrt{93}}{2*-6}=\frac{-18+2\sqrt{93}}{-12}
$