(x^2-9x+8)/(2x-16)=0

Solution for (x^2-9x+8)/(2x-16)=0 equation:

(x^2-9x+8)/(2x-16)=0


Domain of the equation: (2x-16)!=0

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

2x!=16

x!=16/2

x!=8

x∈R


We multiply all the terms by the denominator


(x^2-9x+8)=0

We get rid of parentheses

x^2-9x+8=0

a = 1; b = -9; c = +8;
Δ = b2-4ac
Δ = -92-4·1·8
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-7}{2*1}=\frac{2}{2}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+7}{2*1}=\frac{16}{2}
=8
$