3y-4/2y-1=40

Solution for 3y-4/2y-1=40 equation:

3y-4/2y-1=40

We move all terms to the left:

3y-4/2y-1-(40)=0


Domain of the equation: 2y!=0

y!=0/2

y!=0

y∈R


We add all the numbers together, and all the variables

3y-4/2y-41=0

We multiply all the terms by the denominator


3y*2y-41*2y-4=0

Wy multiply elements

6y^2-82y-4=0

a = 6; b = -82; c = -4;
Δ = b2-4ac
Δ = -822-4·6·(-4)
Δ = 6820
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:

$\sqrt{\Delta}=\sqrt{6820}=\sqrt{4*1705}=\sqrt{4}*\sqrt{1705}=2\sqrt{1705}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-82)-2\sqrt{1705}}{2*6}=\frac{82-2\sqrt{1705}}{12}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-82)+2\sqrt{1705}}{2*6}=\frac{82+2\sqrt{1705}}{12}
$