5/8x-1/4x+1/2=3/10

Solution for 5/8x-1/4x+1/2=3/10 equation:

5/8x-1/4x+1/2=3/10

We move all terms to the left:

5/8x-1/4x+1/2-(3/10)=0


Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R



Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We add all the numbers together, and all the variables

5/8x-1/4x+1/2-(+3/10)=0

We get rid of parentheses

5/8x-1/4x+1/2-3/10=0

We calculate fractions


(-768x^2)/1280x^2+1280x^2/1280x^2+800x/1280x^2+(-320x)/1280x^2=0

Fractions to decimals

(-768x^2)/1280x^2+800x/1280x^2+(-320x)/1280x^2+1=0

We multiply all the terms by the denominator


(-768x^2)+800x+(-320x)+1*1280x^2=0

Wy multiply elements

(-768x^2)+1280x^2+800x+(-320x)=0

We get rid of parentheses

-768x^2+1280x^2+800x-320x=0

We add all the numbers together, and all the variables

512x^2+480x=0

a = 512; b = 480; c = 0;
Δ = b2-4ac
Δ = 4802-4·512·0
Δ = 230400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{230400}=480$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(480)-480}{2*512}=\frac{-960}{1024}
=-15/16
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(480)+480}{2*512}=\frac{0}{1024}
=0
$