1.2m-6=2/3m+10

Solution for 1.2m-6=2/3m+10 equation:

1.2m-6=2/3m+10

We move all terms to the left:

1.2m-6-(2/3m+10)=0


Domain of the equation: 3m+10)!=0

m∈R


We get rid of parentheses

1.2m-2/3m-10-6=0

We multiply all the terms by the denominator


(1.2m)*3m-10*3m-6*3m-2=0

We add all the numbers together, and all the variables

(+1.2m)*3m-10*3m-6*3m-2=0

We multiply parentheses

3m^2-10*3m-6*3m-2=0

Wy multiply elements

3m^2-30m-18m-2=0

We add all the numbers together, and all the variables

3m^2-48m-2=0

a = 3; b = -48; c = -2;
Δ = b2-4ac
Δ = -482-4·3·(-2)
Δ = 2328
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:

$\sqrt{\Delta}=\sqrt{2328}=\sqrt{4*582}=\sqrt{4}*\sqrt{582}=2\sqrt{582}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-48)-2\sqrt{582}}{2*3}=\frac{48-2\sqrt{582}}{6}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-48)+2\sqrt{582}}{2*3}=\frac{48+2\sqrt{582}}{6}
$