6y-3/2y-3=8

Solution for 6y-3/2y-3=8 equation:

6y-3/2y-3=8

We move all terms to the left:

6y-3/2y-3-(8)=0


Domain of the equation: 2y!=0

y!=0/2

y!=0

y∈R


We add all the numbers together, and all the variables

6y-3/2y-11=0

We multiply all the terms by the denominator


6y*2y-11*2y-3=0

Wy multiply elements

12y^2-22y-3=0

a = 12; b = -22; c = -3;
Δ = b2-4ac
Δ = -222-4·12·(-3)
Δ = 628
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:

$\sqrt{\Delta}=\sqrt{628}=\sqrt{4*157}=\sqrt{4}*\sqrt{157}=2\sqrt{157}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-22)-2\sqrt{157}}{2*12}=\frac{22-2\sqrt{157}}{24}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-22)+2\sqrt{157}}{2*12}=\frac{22+2\sqrt{157}}{24}
$