x+8/2x-5=1

Solution for x+8/2x-5=1 equation:

x+8/2x-5=1

We move all terms to the left:

x+8/2x-5-(1)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

x+8/2x-6=0

We multiply all the terms by the denominator


x*2x-6*2x+8=0

Wy multiply elements

2x^2-12x+8=0

a = 2; b = -12; c = +8;
Δ = b2-4ac
Δ = -122-4·2·8
Δ = 80
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{80}=\sqrt{16*5}=\sqrt{16}*\sqrt{5}=4\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-4\sqrt{5}}{2*2}=\frac{12-4\sqrt{5}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+4\sqrt{5}}{2*2}=\frac{12+4\sqrt{5}}{4}
$