8/5x-7/4=3/20x-8

Solution for 8/5x-7/4=3/20x-8 equation:

8/5x-7/4=3/20x-8

We move all terms to the left:

8/5x-7/4-(3/20x-8)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 20x-8)!=0

x∈R


We get rid of parentheses

8/5x-3/20x+8-7/4=0

We calculate fractions


(-1400x^2)/1600x^2+2560x/1600x^2+(-240x)/1600x^2+8=0

We multiply all the terms by the denominator


(-1400x^2)+2560x+(-240x)+8*1600x^2=0

Wy multiply elements

(-1400x^2)+12800x^2+2560x+(-240x)=0

We get rid of parentheses

-1400x^2+12800x^2+2560x-240x=0

We add all the numbers together, and all the variables

11400x^2+2320x=0

a = 11400; b = 2320; c = 0;
Δ = b2-4ac
Δ = 23202-4·11400·0
Δ = 5382400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{5382400}=2320$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2320)-2320}{2*11400}=\frac{-4640}{22800}
=-58/285
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2320)+2320}{2*11400}=\frac{0}{22800}
=0
$