3/4m+7=11/2m-20

Solution for 3/4m+7=11/2m-20 equation:

3/4m+7=11/2m-20

We move all terms to the left:

3/4m+7-(11/2m-20)=0


Domain of the equation: 4m!=0

m!=0/4

m!=0

m∈R



Domain of the equation: 2m-20)!=0

m∈R


We get rid of parentheses

3/4m-11/2m+20+7=0

We calculate fractions


6m/8m^2+(-44m)/8m^2+20+7=0

We add all the numbers together, and all the variables

6m/8m^2+(-44m)/8m^2+27=0

We multiply all the terms by the denominator


6m+(-44m)+27*8m^2=0

Wy multiply elements

216m^2+6m+(-44m)=0

We get rid of parentheses

216m^2+6m-44m=0

We add all the numbers together, and all the variables

216m^2-38m=0

a = 216; b = -38; c = 0;
Δ = b2-4ac
Δ = -382-4·216·0
Δ = 1444
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1444}=38$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-38)-38}{2*216}=\frac{0}{432}
=0
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-38)+38}{2*216}=\frac{76}{432}
=19/108
$