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!=0

y!=0/2

y!=0

y∈R


We add all the numbers together, and all the variables

3y+2/2y-11=0

We multiply all the terms by the denominator


3y*2y-11*2y+2=0

Wy multiply elements

6y^2-22y+2=0

a = 6; b = -22; c = +2;
Δ = b2-4ac
Δ = -222-4·6·2
Δ = 436
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:

$\sqrt{\Delta}=\sqrt{436}=\sqrt{4*109}=\sqrt{4}*\sqrt{109}=2\sqrt{109}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-22)-2\sqrt{109}}{2*6}=\frac{22-2\sqrt{109}}{12}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-22)+2\sqrt{109}}{2*6}=\frac{22+2\sqrt{109}}{12}
$