y/4y+3=2y+13

Solution for y/4y+3=2y+13 equation:

y/4y+3=2y+13

We move all terms to the left:

y/4y+3-(2y+13)=0


Domain of the equation: 4y!=0

y!=0/4

y!=0

y∈R


We get rid of parentheses

y/4y-2y-13+3=0

We multiply all the terms by the denominator


y-2y*4y-13*4y+3*4y=0

Wy multiply elements

-8y^2+y-52y+12y=0

We add all the numbers together, and all the variables

-8y^2-39y=0

a = -8; b = -39; c = 0;
Δ = b2-4ac
Δ = -392-4·(-8)·0
Δ = 1521
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1521}=39$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-39)-39}{2*-8}=\frac{0}{-16}
=0
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-39)+39}{2*-8}=\frac{78}{-16}
=-4+7/8
$