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

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

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

We move all terms to the left:

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


Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R



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

x∈R


We get rid of parentheses

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

We calculate fractions


32x^2/256x^2+96x/256x^2+(-128x)/256x^2-2=0

We multiply all the terms by the denominator


32x^2+96x+(-128x)-2*256x^2=0

Wy multiply elements

32x^2-512x^2+96x+(-128x)=0

We get rid of parentheses

32x^2-512x^2+96x-128x=0

We add all the numbers together, and all the variables

-480x^2-32x=0

a = -480; b = -32; c = 0;
Δ = b2-4ac
Δ = -322-4·(-480)·0
Δ = 1024
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1024}=32$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-32)-32}{2*-480}=\frac{0}{-960}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-32)+32}{2*-480}=\frac{64}{-960}
=-1/15
$