3/5x+1/5=7/20x-4

Solution for 3/5x+1/5=7/20x-4 equation:

3/5x+1/5=7/20x-4

We move all terms to the left:

3/5x+1/5-(7/20x-4)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 20x-4)!=0

x∈R


We get rid of parentheses

3/5x-7/20x+4+1/5=0

We calculate fractions


60x/2500x^2+(-875x)/2500x^2+20x/2500x^2+4=0

We multiply all the terms by the denominator


60x+(-875x)+20x+4*2500x^2=0

We add all the numbers together, and all the variables

80x+(-875x)+4*2500x^2=0

Wy multiply elements

10000x^2+80x+(-875x)=0

We get rid of parentheses

10000x^2+80x-875x=0

We add all the numbers together, and all the variables

10000x^2-795x=0

a = 10000; b = -795; c = 0;
Δ = b2-4ac
Δ = -7952-4·10000·0
Δ = 632025
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{632025}=795$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-795)-795}{2*10000}=\frac{0}{20000}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-795)+795}{2*10000}=\frac{1590}{20000}
=159/2000
$