23x-1/2x+1=9

Solution for 23x-1/2x+1=9 equation:

23x-1/2x+1=9

We move all terms to the left:

23x-1/2x+1-(9)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

23x-1/2x-8=0

We multiply all the terms by the denominator


23x*2x-8*2x-1=0

Wy multiply elements

46x^2-16x-1=0

a = 46; b = -16; c = -1;
Δ = b2-4ac
Δ = -162-4·46·(-1)
Δ = 440
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:

$\sqrt{\Delta}=\sqrt{440}=\sqrt{4*110}=\sqrt{4}*\sqrt{110}=2\sqrt{110}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-2\sqrt{110}}{2*46}=\frac{16-2\sqrt{110}}{92}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+2\sqrt{110}}{2*46}=\frac{16+2\sqrt{110}}{92}
$