3/5y+3=11+5y

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

3/5y+3=11+5y

We move all terms to the left:

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


Domain of the equation: 5y!=0

y!=0/5

y!=0

y∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We multiply all the terms by the denominator


-5y*5y-11*5y+3*5y+3=0

Wy multiply elements

-25y^2-55y+15y+3=0

We add all the numbers together, and all the variables

-25y^2-40y+3=0

a = -25; b = -40; c = +3;
Δ = b2-4ac
Δ = -402-4·(-25)·3
Δ = 1900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1900}=\sqrt{100*19}=\sqrt{100}*\sqrt{19}=10\sqrt{19}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-10\sqrt{19}}{2*-25}=\frac{40-10\sqrt{19}}{-50}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+10\sqrt{19}}{2*-25}=\frac{40+10\sqrt{19}}{-50}
$