-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

384x^2-80x=0

a = 384; b = -80; c = 0;
Δ = b2-4ac
Δ = -802-4·384·0
Δ = 6400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{6400}=80$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-80)-80}{2*384}=\frac{0}{768}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-80)+80}{2*384}=\frac{160}{768}
=5/24
$