6y-9/2y-5=8y+17+4y

Solution for 6y-9/2y-5=8y+17+4y equation:

6y-9/2y-5=8y+17+4y

We move all terms to the left:

6y-9/2y-5-(8y+17+4y)=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-9/2y-(12y+17)-5=0

We get rid of parentheses

6y-9/2y-12y-17-5=0

We multiply all the terms by the denominator


6y*2y-12y*2y-17*2y-5*2y-9=0

Wy multiply elements

12y^2-24y^2-34y-10y-9=0

We add all the numbers together, and all the variables

-12y^2-44y-9=0

a = -12; b = -44; c = -9;
Δ = b2-4ac
Δ = -442-4·(-12)·(-9)
Δ = 1504
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:

$\sqrt{\Delta}=\sqrt{1504}=\sqrt{16*94}=\sqrt{16}*\sqrt{94}=4\sqrt{94}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-44)-4\sqrt{94}}{2*-12}=\frac{44-4\sqrt{94}}{-24}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-44)+4\sqrt{94}}{2*-12}=\frac{44+4\sqrt{94}}{-24}
$