(X-2)(3x+4)/(x+3)=0

Solution for (X-2)(3x+4)/(x+3)=0 equation:

(X-2)(3X+4)/(X+3)=0


Domain of the equation: (X+3)!=0

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

X!=-3

X∈R


We multiply parentheses ..

(+3X^2+4X-6X-8)/(X+3)=0

We multiply all the terms by the denominator


(+3X^2+4X-6X-8)=0

We get rid of parentheses

3X^2+4X-6X-8=0

We add all the numbers together, and all the variables

3X^2-2X-8=0

a = 3; b = -2; c = -8;
Δ = b2-4ac
Δ = -22-4·3·(-8)
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*3}=\frac{-8}{6}
=-1+1/3
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+10}{2*3}=\frac{12}{6}
=2
$