9m+15-2=29/4m+1

Solution for 9m+15-2=29/4m+1 equation:

9m+15-2=29/4m+1

We move all terms to the left:

9m+15-2-(29/4m+1)=0


Domain of the equation: 4m+1)!=0

m∈R


We add all the numbers together, and all the variables

9m-(29/4m+1)+13=0

We get rid of parentheses

9m-29/4m-1+13=0

We multiply all the terms by the denominator


9m*4m-1*4m+13*4m-29=0

Wy multiply elements

36m^2-4m+52m-29=0

We add all the numbers together, and all the variables

36m^2+48m-29=0

a = 36; b = 48; c = -29;
Δ = b2-4ac
Δ = 482-4·36·(-29)
Δ = 6480
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:

$\sqrt{\Delta}=\sqrt{6480}=\sqrt{1296*5}=\sqrt{1296}*\sqrt{5}=36\sqrt{5}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(48)-36\sqrt{5}}{2*36}=\frac{-48-36\sqrt{5}}{72}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(48)+36\sqrt{5}}{2*36}=\frac{-48+36\sqrt{5}}{72}
$