33/2+3/5y=7/10y+15

Solution for 33/2+3/5y=7/10y+15 equation:

33/2+3/5y=7/10y+15

We move all terms to the left:

33/2+3/5y-(7/10y+15)=0


Domain of the equation: 5y!=0

y!=0/5

y!=0

y∈R



Domain of the equation: 10y+15)!=0

y∈R


We get rid of parentheses

3/5y-7/10y-15+33/2=0

We calculate fractions


1650y^2/200y^2+120y/200y^2+(-140y)/200y^2-15=0

We multiply all the terms by the denominator


1650y^2+120y+(-140y)-15*200y^2=0

Wy multiply elements

1650y^2-3000y^2+120y+(-140y)=0

We get rid of parentheses

1650y^2-3000y^2+120y-140y=0

We add all the numbers together, and all the variables

-1350y^2-20y=0

a = -1350; b = -20; c = 0;
Δ = b2-4ac
Δ = -202-4·(-1350)·0
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-20}{2*-1350}=\frac{0}{-2700}
=0
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+20}{2*-1350}=\frac{40}{-2700}
=-2/135
$