(2y^2-14y+20)/(y^2+5y-14)=0

Solution for (2y^2-14y+20)/(y^2+5y-14)=0 equation:

(2y^2-14y+20)/(y^2+5y-14)=0


Domain of the equation: (y^2+5y-14)!=0

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

y^2+5y!=14

y∈R


We multiply all the terms by the denominator


(2y^2-14y+20)=0

We get rid of parentheses

2y^2-14y+20=0

a = 2; b = -14; c = +20;
Δ = b2-4ac
Δ = -142-4·2·20
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-6}{2*2}=\frac{8}{4}
=2
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+6}{2*2}=\frac{20}{4}
=5
$