2/3m+2=6m-3

Solution for 2/3m+2=6m-3 equation:

2/3m+2=6m-3

We move all terms to the left:

2/3m+2-(6m-3)=0


Domain of the equation: 3m!=0

m!=0/3

m!=0

m∈R


We get rid of parentheses

2/3m-6m+3+2=0

We multiply all the terms by the denominator


-6m*3m+3*3m+2*3m+2=0

Wy multiply elements

-18m^2+9m+6m+2=0

We add all the numbers together, and all the variables

-18m^2+15m+2=0

a = -18; b = 15; c = +2;
Δ = b2-4ac
Δ = 152-4·(-18)·2
Δ = 369
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:

$\sqrt{\Delta}=\sqrt{369}=\sqrt{9*41}=\sqrt{9}*\sqrt{41}=3\sqrt{41}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-3\sqrt{41}}{2*-18}=\frac{-15-3\sqrt{41}}{-36}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+3\sqrt{41}}{2*-18}=\frac{-15+3\sqrt{41}}{-36}
$