3y+2/(2y-7)=4

Solution for 3y+2/(2y-7)=4 equation:

3y+2/(2y-7)=4

We move all terms to the left:

3y+2/(2y-7)-(4)=0


Domain of the equation: (2y-7)!=0

We move all terms containing y to the left, all other terms to the right

2y!=7

y!=7/2

y!=3+1/2

y∈R


We multiply all the terms by the denominator


3y*(2y-7)-4*(2y-7)+2=0

We multiply parentheses

6y^2-21y-8y+28+2=0

We add all the numbers together, and all the variables

6y^2-29y+30=0

a = 6; b = -29; c = +30;
Δ = b2-4ac
Δ = -292-4·6·30
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{-(-29)-11}{2*6}=\frac{18}{12}
=1+1/2
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-29)+11}{2*6}=\frac{40}{12}
=3+1/3
$