3/6m+6=4m+25

Solution for 3/6m+6=4m+25 equation:

3/6m+6=4m+25

We move all terms to the left:

3/6m+6-(4m+25)=0


Domain of the equation: 6m!=0

m!=0/6

m!=0

m∈R


We get rid of parentheses

3/6m-4m-25+6=0

We multiply all the terms by the denominator


-4m*6m-25*6m+6*6m+3=0

Wy multiply elements

-24m^2-150m+36m+3=0

We add all the numbers together, and all the variables

-24m^2-114m+3=0

a = -24; b = -114; c = +3;
Δ = b2-4ac
Δ = -1142-4·(-24)·3
Δ = 13284
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:

$\sqrt{\Delta}=\sqrt{13284}=\sqrt{324*41}=\sqrt{324}*\sqrt{41}=18\sqrt{41}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-114)-18\sqrt{41}}{2*-24}=\frac{114-18\sqrt{41}}{-48}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-114)+18\sqrt{41}}{2*-24}=\frac{114+18\sqrt{41}}{-48}
$