15m-11=7/4m+1

Solution for 15m-11=7/4m+1 equation:

15m-11=7/4m+1

We move all terms to the left:

15m-11-(7/4m+1)=0


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

m∈R


We get rid of parentheses

15m-7/4m-1-11=0

We multiply all the terms by the denominator


15m*4m-1*4m-11*4m-7=0

Wy multiply elements

60m^2-4m-44m-7=0

We add all the numbers together, and all the variables

60m^2-48m-7=0

a = 60; b = -48; c = -7;
Δ = b2-4ac
Δ = -482-4·60·(-7)
Δ = 3984
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:

$\sqrt{\Delta}=\sqrt{3984}=\sqrt{16*249}=\sqrt{16}*\sqrt{249}=4\sqrt{249}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-48)-4\sqrt{249}}{2*60}=\frac{48-4\sqrt{249}}{120}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-48)+4\sqrt{249}}{2*60}=\frac{48+4\sqrt{249}}{120}
$