m+3/m-2+5m-35/m-2=5/m-8

Solution for m+3/m-2+5m-35/m-2=5/m-8 equation:

m+3/m-2+5m-35/m-2=5/m-8

We move all terms to the left:

m+3/m-2+5m-35/m-2-(5/m-8)=0


Domain of the equation: m!=0

m∈R



Domain of the equation: m-8)!=0

m∈R


We add all the numbers together, and all the variables

6m+3/m-35/m-(5/m-8)-4=0

We get rid of parentheses

6m+3/m-35/m-5/m+8-4=0

We multiply all the terms by the denominator


6m*m+8*m-4*m+3-35-5=0

We add all the numbers together, and all the variables

4m+6m*m-37=0

Wy multiply elements

6m^2+4m-37=0

a = 6; b = 4; c = -37;
Δ = b2-4ac
Δ = 42-4·6·(-37)
Δ = 904
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:

$\sqrt{\Delta}=\sqrt{904}=\sqrt{4*226}=\sqrt{4}*\sqrt{226}=2\sqrt{226}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-2\sqrt{226}}{2*6}=\frac{-4-2\sqrt{226}}{12}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+2\sqrt{226}}{2*6}=\frac{-4+2\sqrt{226}}{12}
$