(y^2-7y+12)/(6y^2+6y-72)=0

Solution for (y^2-7y+12)/(6y^2+6y-72)=0 equation:

(y^2-7y+12)/(6y^2+6y-72)=0


Domain of the equation: (6y^2+6y-72)!=0

We move all terms containing y to the left, all other terms to the right

6y^2+6y!=72

y∈R


We multiply all the terms by the denominator


(y^2-7y+12)=0

We get rid of parentheses

y^2-7y+12=0

a = 1; b = -7; c = +12;
Δ = b2-4ac
Δ = -72-4·1·12
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-1}{2*1}=\frac{6}{2}
=3
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+1}{2*1}=\frac{8}{2}
=4
$