x+1/2x+8=23

Solution for x+1/2x+8=23 equation:

x+1/2x+8=23

We move all terms to the left:

x+1/2x+8-(23)=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+1/2x-15=0

We multiply all the terms by the denominator


x*2x-15*2x+1=0

Wy multiply elements

2x^2-30x+1=0

a = 2; b = -30; c = +1;
Δ = b2-4ac
Δ = -302-4·2·1
Δ = 892
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:

$\sqrt{\Delta}=\sqrt{892}=\sqrt{4*223}=\sqrt{4}*\sqrt{223}=2\sqrt{223}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-2\sqrt{223}}{2*2}=\frac{30-2\sqrt{223}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+2\sqrt{223}}{2*2}=\frac{30+2\sqrt{223}}{4}
$