(5x^2-18x-27)/(x-5)=0

Solution for (5x^2-18x-27)/(x-5)=0 equation:

(5x^2-18x-27)/(x-5)=0


Domain of the equation: (x-5)!=0

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

x!=5

x∈R


We multiply all the terms by the denominator


(5x^2-18x-27)=0

We get rid of parentheses

5x^2-18x-27=0

a = 5; b = -18; c = -27;
Δ = b2-4ac
Δ = -182-4·5·(-27)
Δ = 864
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{864}=\sqrt{144*6}=\sqrt{144}*\sqrt{6}=12\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-12\sqrt{6}}{2*5}=\frac{18-12\sqrt{6}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+12\sqrt{6}}{2*5}=\frac{18+12\sqrt{6}}{10}
$