3y-12/y-4=6

Solution for 3y-12/y-4=6 equation:

3y-12/y-4=6

We move all terms to the left:

3y-12/y-4-(6)=0


Domain of the equation: y!=0

y∈R


We add all the numbers together, and all the variables

3y-12/y-10=0

We multiply all the terms by the denominator


3y*y-10*y-12=0

We add all the numbers together, and all the variables

-10y+3y*y-12=0

Wy multiply elements

3y^2-10y-12=0

a = 3; b = -10; c = -12;
Δ = b2-4ac
Δ = -102-4·3·(-12)
Δ = 244
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:

$\sqrt{\Delta}=\sqrt{244}=\sqrt{4*61}=\sqrt{4}*\sqrt{61}=2\sqrt{61}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{61}}{2*3}=\frac{10-2\sqrt{61}}{6}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{61}}{2*3}=\frac{10+2\sqrt{61}}{6}
$