9/5y-3=3/10y+6

Solution for 9/5y-3=3/10y+6 equation:

9/5y-3=3/10y+6

We move all terms to the left:

9/5y-3-(3/10y+6)=0


Domain of the equation: 5y!=0

y!=0/5

y!=0

y∈R



Domain of the equation: 10y+6)!=0

y∈R


We get rid of parentheses

9/5y-3/10y-6-3=0

We calculate fractions


90y/50y^2+(-15y)/50y^2-6-3=0

We add all the numbers together, and all the variables

90y/50y^2+(-15y)/50y^2-9=0

We multiply all the terms by the denominator


90y+(-15y)-9*50y^2=0

Wy multiply elements

-450y^2+90y+(-15y)=0

We get rid of parentheses

-450y^2+90y-15y=0

We add all the numbers together, and all the variables

-450y^2+75y=0

a = -450; b = 75; c = 0;
Δ = b2-4ac
Δ = 752-4·(-450)·0
Δ = 5625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{5625}=75$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(75)-75}{2*-450}=\frac{-150}{-900}
=1/6
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(75)+75}{2*-450}=\frac{0}{-900}
=0
$