5/8m-1/2m+1=5

Solution for 5/8m-1/2m+1=5 equation:

5/8m-1/2m+1=5

We move all terms to the left:

5/8m-1/2m+1-(5)=0


Domain of the equation: 8m!=0

m!=0/8

m!=0

m∈R



Domain of the equation: 2m!=0

m!=0/2

m!=0

m∈R


We add all the numbers together, and all the variables

5/8m-1/2m-4=0

We calculate fractions


10m/16m^2+(-8m)/16m^2-4=0

We multiply all the terms by the denominator


10m+(-8m)-4*16m^2=0

Wy multiply elements

-64m^2+10m+(-8m)=0

We get rid of parentheses

-64m^2+10m-8m=0

We add all the numbers together, and all the variables

-64m^2+2m=0

a = -64; b = 2; c = 0;
Δ = b2-4ac
Δ = 22-4·(-64)·0
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2}{2*-64}=\frac{-4}{-128}
=1/32
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2}{2*-64}=\frac{0}{-128}
=0
$