y/2y+3=5y-9

Solution for y/2y+3=5y-9 equation:

y/2y+3=5y-9

We move all terms to the left:

y/2y+3-(5y-9)=0


Domain of the equation: 2y!=0

y!=0/2

y!=0

y∈R


We get rid of parentheses

y/2y-5y+9+3=0

We multiply all the terms by the denominator


y-5y*2y+9*2y+3*2y=0

Wy multiply elements

-10y^2+y+18y+6y=0

We add all the numbers together, and all the variables

-10y^2+25y=0

a = -10; b = 25; c = 0;
Δ = b2-4ac
Δ = 252-4·(-10)·0
Δ = 625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{625}=25$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(25)-25}{2*-10}=\frac{-50}{-20}
=2+1/2
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(25)+25}{2*-10}=\frac{0}{-20}
=0
$