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

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

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

We move all terms to the left:

3/5x+1/4-(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+1/4=0

We calculate fractions


200x^2/1600x^2+960x/1600x^2+(-560x)/1600x^2+4=0

We multiply all the terms by the denominator


200x^2+960x+(-560x)+4*1600x^2=0

Wy multiply elements

200x^2+6400x^2+960x+(-560x)=0

We get rid of parentheses

200x^2+6400x^2+960x-560x=0

We add all the numbers together, and all the variables

6600x^2+400x=0

a = 6600; b = 400; c = 0;
Δ = b2-4ac
Δ = 4002-4·6600·0
Δ = 160000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{160000}=400$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(400)-400}{2*6600}=\frac{-800}{13200}
=-2/33
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(400)+400}{2*6600}=\frac{0}{13200}
=0
$