(2x2+2x-12)/(x-2)=0

Solution for (2x2+2x-12)/(x-2)=0 equation:

(2x^2+2x-12)/(x-2)=0


Domain of the equation: (x-2)!=0

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

x!=2

x∈R


We multiply all the terms by the denominator


(2x^2+2x-12)=0

We get rid of parentheses

2x^2+2x-12=0

a = 2; b = 2; c = -12;
Δ = b2-4ac
Δ = 22-4·2·(-12)
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-10}{2*2}=\frac{-12}{4}
=-3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+10}{2*2}=\frac{8}{4}
=2
$