3/5y-6=1/4y+10

Solution for 3/5y-6=1/4y+10 equation:

3/5y-6=1/4y+10

We move all terms to the left:

3/5y-6-(1/4y+10)=0


Domain of the equation: 5y!=0

y!=0/5

y!=0

y∈R



Domain of the equation: 4y+10)!=0

y∈R


We get rid of parentheses

3/5y-1/4y-10-6=0

We calculate fractions


12y/20y^2+(-5y)/20y^2-10-6=0

We add all the numbers together, and all the variables

12y/20y^2+(-5y)/20y^2-16=0

We multiply all the terms by the denominator


12y+(-5y)-16*20y^2=0

Wy multiply elements

-320y^2+12y+(-5y)=0

We get rid of parentheses

-320y^2+12y-5y=0

We add all the numbers together, and all the variables

-320y^2+7y=0

a = -320; b = 7; c = 0;
Δ = b2-4ac
Δ = 72-4·(-320)·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*-320}=\frac{-14}{-640}
=7/320
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+7}{2*-320}=\frac{0}{-640}
=0
$