3/5y=3y-4

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

3/5y=3y-4

We move all terms to the left:

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


Domain of the equation: 5y!=0

y!=0/5

y!=0

y∈R


We get rid of parentheses

3/5y-3y+4=0

We multiply all the terms by the denominator


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

Wy multiply elements

-15y^2+20y+3=0

a = -15; b = 20; c = +3;
Δ = b2-4ac
Δ = 202-4·(-15)·3
Δ = 580
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:

$\sqrt{\Delta}=\sqrt{580}=\sqrt{4*145}=\sqrt{4}*\sqrt{145}=2\sqrt{145}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-2\sqrt{145}}{2*-15}=\frac{-20-2\sqrt{145}}{-30}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+2\sqrt{145}}{2*-15}=\frac{-20+2\sqrt{145}}{-30}
$