1/4m+5=3/8m+4

Solution for 1/4m+5=3/8m+4 equation:

1/4m+5=3/8m+4

We move all terms to the left:

1/4m+5-(3/8m+4)=0


Domain of the equation: 4m!=0

m!=0/4

m!=0

m∈R



Domain of the equation: 8m+4)!=0

m∈R


We get rid of parentheses

1/4m-3/8m-4+5=0

We calculate fractions


8m/32m^2+(-12m)/32m^2-4+5=0

We add all the numbers together, and all the variables

8m/32m^2+(-12m)/32m^2+1=0

We multiply all the terms by the denominator


8m+(-12m)+1*32m^2=0

Wy multiply elements

32m^2+8m+(-12m)=0

We get rid of parentheses

32m^2+8m-12m=0

We add all the numbers together, and all the variables

32m^2-4m=0

a = 32; b = -4; c = 0;
Δ = b2-4ac
Δ = -42-4·32·0
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*32}=\frac{0}{64}
=0
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4}{2*32}=\frac{8}{64}
=1/8
$