(x^2-2x-15)/(x-7)=0

Solution for (x^2-2x-15)/(x-7)=0 equation:

(x^2-2x-15)/(x-7)=0


Domain of the equation: (x-7)!=0

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

x!=7

x∈R


We multiply all the terms by the denominator


(x^2-2x-15)=0

We get rid of parentheses

x^2-2x-15=0

a = 1; b = -2; c = -15;
Δ = b2-4ac
Δ = -22-4·1·(-15)
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-8}{2*1}=\frac{-6}{2}
=-3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+8}{2*1}=\frac{10}{2}
=5
$