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

We get rid of parentheses

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

We calculate fractions


8y/20y^2+(-15y)/20y^2-20-8=0

We add all the numbers together, and all the variables

8y/20y^2+(-15y)/20y^2-28=0

We multiply all the terms by the denominator


8y+(-15y)-28*20y^2=0

Wy multiply elements

-560y^2+8y+(-15y)=0

We get rid of parentheses

-560y^2+8y-15y=0

We add all the numbers together, and all the variables

-560y^2-7y=0

a = -560; b = -7; c = 0;
Δ = b2-4ac
Δ = -72-4·(-560)·0
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-7}{2*-560}=\frac{0}{-1120}
=0
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+7}{2*-560}=\frac{14}{-1120}
=-1/80
$