3/5y-4=16-20y

Solution for 3/5y-4=16-20y equation:

3/5y-4=16-20y

We move all terms to the left:

3/5y-4-(16-20y)=0


Domain of the equation: 5y!=0

y!=0/5

y!=0

y∈R


We add all the numbers together, and all the variables

3/5y-(-20y+16)-4=0

We get rid of parentheses

3/5y+20y-16-4=0

We multiply all the terms by the denominator


20y*5y-16*5y-4*5y+3=0

Wy multiply elements

100y^2-80y-20y+3=0

We add all the numbers together, and all the variables

100y^2-100y+3=0

a = 100; b = -100; c = +3;
Δ = b2-4ac
Δ = -1002-4·100·3
Δ = 8800
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{8800}=\sqrt{400*22}=\sqrt{400}*\sqrt{22}=20\sqrt{22}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-100)-20\sqrt{22}}{2*100}=\frac{100-20\sqrt{22}}{200}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-100)+20\sqrt{22}}{2*100}=\frac{100+20\sqrt{22}}{200}
$