2/5y-8=20*3/4y

Solution for 2/5y-8=20*3/4y equation:

2/5y-8=20*3/4y

We move all terms to the left:

2/5y-8-(20*3/4y)=0


Domain of the equation: 5y!=0

y!=0/5

y!=0

y∈R



Domain of the equation: 4y)!=0

y!=0/1

y!=0

y∈R


We add all the numbers together, and all the variables

2/5y-(+20*3/4y)-8=0

We get rid of parentheses

2/5y-20*3/4y-8=0

We calculate fractions


8y/20y^2+(-1500y)/20y^2-8=0

We multiply all the terms by the denominator


8y+(-1500y)-8*20y^2=0

Wy multiply elements

-160y^2+8y+(-1500y)=0

We get rid of parentheses

-160y^2+8y-1500y=0

We add all the numbers together, and all the variables

-160y^2-1492y=0

a = -160; b = -1492; c = 0;
Δ = b2-4ac
Δ = -14922-4·(-160)·0
Δ = 2226064
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2226064}=1492$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1492)-1492}{2*-160}=\frac{0}{-320}
=0
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1492)+1492}{2*-160}=\frac{2984}{-320}
=-9+13/40
$