3/5y-1=12/25y+8

Solution for 3/5y-1=12/25y+8 equation:

3/5y-1=12/25y+8

We move all terms to the left:

3/5y-1-(12/25y+8)=0


Domain of the equation: 5y!=0

y!=0/5

y!=0

y∈R



Domain of the equation: 25y+8)!=0

y∈R


We get rid of parentheses

3/5y-12/25y-8-1=0

We calculate fractions


75y/125y^2+(-60y)/125y^2-8-1=0

We add all the numbers together, and all the variables

75y/125y^2+(-60y)/125y^2-9=0

We multiply all the terms by the denominator


75y+(-60y)-9*125y^2=0

Wy multiply elements

-1125y^2+75y+(-60y)=0

We get rid of parentheses

-1125y^2+75y-60y=0

We add all the numbers together, and all the variables

-1125y^2+15y=0

a = -1125; b = 15; c = 0;
Δ = b2-4ac
Δ = 152-4·(-1125)·0
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-15}{2*-1125}=\frac{-30}{-2250}
=1/75
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+15}{2*-1125}=\frac{0}{-2250}
=0
$