(x^2-5x-14)/(x-7)=0

Solution for (x^2-5x-14)/(x-7)=0 equation:

(x^2-5x-14)/(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^2-5x-14)=0

We get rid of parentheses

x^2-5x-14=0

a = 1; b = -5; c = -14;
Δ = b2-4ac
Δ = -52-4·1·(-14)
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-9}{2*1}=\frac{-4}{2}
=-2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+9}{2*1}=\frac{14}{2}
=7
$