7/8m-1/5=3/16m+5

Solution for 7/8m-1/5=3/16m+5 equation:

7/8m-1/5=3/16m+5

We move all terms to the left:

7/8m-1/5-(3/16m+5)=0


Domain of the equation: 8m!=0

m!=0/8

m!=0

m∈R



Domain of the equation: 16m+5)!=0

m∈R


We get rid of parentheses

7/8m-3/16m-5-1/5=0

We calculate fractions


(-128m^2)/3200m^2+2800m/3200m^2+(-600m)/3200m^2-5=0

We multiply all the terms by the denominator


(-128m^2)+2800m+(-600m)-5*3200m^2=0

Wy multiply elements

(-128m^2)-16000m^2+2800m+(-600m)=0

We get rid of parentheses

-128m^2-16000m^2+2800m-600m=0

We add all the numbers together, and all the variables

-16128m^2+2200m=0

a = -16128; b = 2200; c = 0;
Δ = b2-4ac
Δ = 22002-4·(-16128)·0
Δ = 4840000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4840000}=2200$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2200)-2200}{2*-16128}=\frac{-4400}{-32256}
=275/2016
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2200)+2200}{2*-16128}=\frac{0}{-32256}
=0
$