15+2/9m=8+m

Solution for 15+2/9m=8+m equation:

15+2/9m=8+m

We move all terms to the left:

15+2/9m-(8+m)=0


Domain of the equation: 9m!=0

m!=0/9

m!=0

m∈R


We add all the numbers together, and all the variables

2/9m-(m+8)+15=0

We get rid of parentheses

2/9m-m-8+15=0

We multiply all the terms by the denominator


-m*9m-8*9m+15*9m+2=0

Wy multiply elements

-9m^2-72m+135m+2=0

We add all the numbers together, and all the variables

-9m^2+63m+2=0

a = -9; b = 63; c = +2;
Δ = b2-4ac
Δ = 632-4·(-9)·2
Δ = 4041
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:

$\sqrt{\Delta}=\sqrt{4041}=\sqrt{9*449}=\sqrt{9}*\sqrt{449}=3\sqrt{449}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(63)-3\sqrt{449}}{2*-9}=\frac{-63-3\sqrt{449}}{-18}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(63)+3\sqrt{449}}{2*-9}=\frac{-63+3\sqrt{449}}{-18}
$