1/8m+7=2+3/4m

Solution for 1/8m+7=2+3/4m equation:

1/8m+7=2+3/4m

We move all terms to the left:

1/8m+7-(2+3/4m)=0


Domain of the equation: 8m!=0

m!=0/8

m!=0

m∈R



Domain of the equation: 4m)!=0

m!=0/1

m!=0

m∈R


We add all the numbers together, and all the variables

1/8m-(3/4m+2)+7=0

We get rid of parentheses

1/8m-3/4m-2+7=0

We calculate fractions


4m/32m^2+(-24m)/32m^2-2+7=0

We add all the numbers together, and all the variables

4m/32m^2+(-24m)/32m^2+5=0

We multiply all the terms by the denominator


4m+(-24m)+5*32m^2=0

Wy multiply elements

160m^2+4m+(-24m)=0

We get rid of parentheses

160m^2+4m-24m=0

We add all the numbers together, and all the variables

160m^2-20m=0

a = 160; b = -20; c = 0;
Δ = b2-4ac
Δ = -202-4·160·0
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-20}{2*160}=\frac{0}{320}
=0
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+20}{2*160}=\frac{40}{320}
=1/8
$