(8y^2-15y-2)/(y^2+5y-14)=0

Solution for (8y^2-15y-2)/(y^2+5y-14)=0 equation:

(8y^2-15y-2)/(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


(8y^2-15y-2)=0

We get rid of parentheses

8y^2-15y-2=0

a = 8; b = -15; c = -2;
Δ = b2-4ac
Δ = -152-4·8·(-2)
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-17}{2*8}=\frac{-2}{16}
=-1/8
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+17}{2*8}=\frac{32}{16}
=2
$