1/5x-1/4=1/2x+2

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

1/5x-1/4=1/2x+2

We move all terms to the left:

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


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



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

x∈R


We get rid of parentheses

1/5x-1/2x-2-1/4=0

We calculate fractions


(-20x^2)/160x^2+32x/160x^2+(-80x)/160x^2-2=0

We multiply all the terms by the denominator


(-20x^2)+32x+(-80x)-2*160x^2=0

Wy multiply elements

(-20x^2)-320x^2+32x+(-80x)=0

We get rid of parentheses

-20x^2-320x^2+32x-80x=0

We add all the numbers together, and all the variables

-340x^2-48x=0

a = -340; b = -48; c = 0;
Δ = b2-4ac
Δ = -482-4·(-340)·0
Δ = 2304
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2304}=48$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-48)-48}{2*-340}=\frac{0}{-680}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-48)+48}{2*-340}=\frac{96}{-680}
=-12/85
$