6/5m+8+9/5m=5+3m

Solution for 6/5m+8+9/5m=5+3m equation:

6/5m+8+9/5m=5+3m

We move all terms to the left:

6/5m+8+9/5m-(5+3m)=0


Domain of the equation: 5m!=0

m!=0/5

m!=0

m∈R


We add all the numbers together, and all the variables

6/5m+9/5m-(3m+5)+8=0

We get rid of parentheses

6/5m+9/5m-3m-5+8=0

We multiply all the terms by the denominator


-3m*5m-5*5m+8*5m+6+9=0

We add all the numbers together, and all the variables

-3m*5m-5*5m+8*5m+15=0

Wy multiply elements

-15m^2-25m+40m+15=0

We add all the numbers together, and all the variables

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

a = -15; b = 15; c = +15;
Δ = b2-4ac
Δ = 152-4·(-15)·15
Δ = 1125
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:

$\sqrt{\Delta}=\sqrt{1125}=\sqrt{225*5}=\sqrt{225}*\sqrt{5}=15\sqrt{5}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-15\sqrt{5}}{2*-15}=\frac{-15-15\sqrt{5}}{-30}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+15\sqrt{5}}{2*-15}=\frac{-15+15\sqrt{5}}{-30}
$