0=3y-6/8y-9

Solution for 0=3y-6/8y-9 equation:

0=3y-6/8y-9

We move all terms to the left:

0-(3y-6/8y-9)=0


Domain of the equation: 8y-9)!=0

y∈R


We add all the numbers together, and all the variables

-(3y-6/8y-9)=0

We get rid of parentheses

-3y+6/8y+9=0

We multiply all the terms by the denominator


-3y*8y+9*8y+6=0

Wy multiply elements

-24y^2+72y+6=0

a = -24; b = 72; c = +6;
Δ = b2-4ac
Δ = 722-4·(-24)·6
Δ = 5760
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:

$\sqrt{\Delta}=\sqrt{5760}=\sqrt{576*10}=\sqrt{576}*\sqrt{10}=24\sqrt{10}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(72)-24\sqrt{10}}{2*-24}=\frac{-72-24\sqrt{10}}{-48}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(72)+24\sqrt{10}}{2*-24}=\frac{-72+24\sqrt{10}}{-48}
$