(x^2+11x-27)/(x+7)=0

Solution for (x^2+11x-27)/(x+7)=0 equation:

(x^2+11x-27)/(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+11x-27)=0

We get rid of parentheses

x^2+11x-27=0

a = 1; b = 11; c = -27;
Δ = b2-4ac
Δ = 112-4·1·(-27)
Δ = 229
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-\sqrt{229}}{2*1}=\frac{-11-\sqrt{229}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+\sqrt{229}}{2*1}=\frac{-11+\sqrt{229}}{2}
$