3/4y+3=11+1/5y

Solution for 3/4y+3=11+1/5y equation:

3/4y+3=11+1/5y

We move all terms to the left:

3/4y+3-(11+1/5y)=0


Domain of the equation: 4y!=0

y!=0/4

y!=0

y∈R



Domain of the equation: 5y)!=0

y!=0/1

y!=0

y∈R


We add all the numbers together, and all the variables

3/4y-(1/5y+11)+3=0

We get rid of parentheses

3/4y-1/5y-11+3=0

We calculate fractions


15y/20y^2+(-4y)/20y^2-11+3=0

We add all the numbers together, and all the variables

15y/20y^2+(-4y)/20y^2-8=0

We multiply all the terms by the denominator


15y+(-4y)-8*20y^2=0

Wy multiply elements

-160y^2+15y+(-4y)=0

We get rid of parentheses

-160y^2+15y-4y=0

We add all the numbers together, and all the variables

-160y^2+11y=0

a = -160; b = 11; c = 0;
Δ = b2-4ac
Δ = 112-4·(-160)·0
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-11}{2*-160}=\frac{-22}{-320}
=11/160
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+11}{2*-160}=\frac{0}{-320}
=0
$