2x-8/(x-3)=0

Solution for 2x-8/(x-3)=0 equation:

2x-8/(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 all the terms by the denominator


2x*(x-3)-8=0

We multiply parentheses

2x^2-6x-8=0

a = 2; b = -6; c = -8;
Δ = b2-4ac
Δ = -62-4·2·(-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{-(-6)-10}{2*2}=\frac{-4}{4}
=-1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+10}{2*2}=\frac{16}{4}
=4
$