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

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

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

We move all terms to the left:

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


Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R



Domain of the equation: 4x+5)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


4x/32x^2+(-8x)/32x^2-5+3=0

We add all the numbers together, and all the variables

4x/32x^2+(-8x)/32x^2-2=0

We multiply all the terms by the denominator


4x+(-8x)-2*32x^2=0

Wy multiply elements

-64x^2+4x+(-8x)=0

We get rid of parentheses

-64x^2+4x-8x=0

We add all the numbers together, and all the variables

-64x^2-4x=0

a = -64; b = -4; c = 0;
Δ = b2-4ac
Δ = -42-4·(-64)·0
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4}{2*-64}=\frac{0}{-128}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4}{2*-64}=\frac{8}{-128}
=-1/16
$