3/8x+1/2=1/4x+2

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

3/8x+1/2=1/4x+2

We move all terms to the left:

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


Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R



Domain of the equation: 4x+2)!=0

x∈R


We get rid of parentheses

3/8x-1/4x-2+1/2=0

We calculate fractions


128x^2/128x^2+48x/128x^2+(-32x)/128x^2-2=0

Fractions to decimals

48x/128x^2+(-32x)/128x^2-2+1=0

We multiply all the terms by the denominator


48x+(-32x)-2*128x^2+1*128x^2=0

Wy multiply elements

-256x^2+128x^2+48x+(-32x)=0

We get rid of parentheses

-256x^2+128x^2+48x-32x=0

We add all the numbers together, and all the variables

-128x^2+16x=0

a = -128; b = 16; c = 0;
Δ = b2-4ac
Δ = 162-4·(-128)·0
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-16}{2*-128}=\frac{-32}{-256}
=1/8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+16}{2*-128}=\frac{0}{-256}
=0
$