15/8*m-11=7/4*m+1

Solution for 15/8*m-11=7/4*m+1 equation:

15/8m-11=7/4m+1

We move all terms to the left:

15/8m-11-(7/4m+1)=0


Domain of the equation: 8m!=0

m!=0/8

m!=0

m∈R



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

m∈R


We get rid of parentheses

15/8m-7/4m-1-11=0

We calculate fractions


60m/32m^2+(-56m)/32m^2-1-11=0

We add all the numbers together, and all the variables

60m/32m^2+(-56m)/32m^2-12=0

We multiply all the terms by the denominator


60m+(-56m)-12*32m^2=0

Wy multiply elements

-384m^2+60m+(-56m)=0

We get rid of parentheses

-384m^2+60m-56m=0

We add all the numbers together, and all the variables

-384m^2+4m=0

a = -384; b = 4; c = 0;
Δ = b2-4ac
Δ = 42-4·(-384)·0
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4}{2*-384}=\frac{-8}{-768}
=1/96
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4}{2*-384}=\frac{0}{-768}
=0
$