x^2/(x-6)+3=0

Solution for x^2/(x-6)+3=0 equation:

x^2/(x-6)+3=0


Domain of the equation: (x-6)!=0

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

x!=6

x∈R


We multiply all the terms by the denominator


x^2+3*(x-6)=0

We multiply parentheses

x^2+3x-18=0

a = 1; b = 3; c = -18;
Δ = b2-4ac
Δ = 32-4·1·(-18)
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{-(3)-9}{2*1}=\frac{-12}{2}
=-6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+9}{2*1}=\frac{6}{2}
=3
$