3x-1/8x=23

Solution for 3x-1/8x=23 equation:

3x-1/8x=23

We move all terms to the left:

3x-1/8x-(23)=0


Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R


We multiply all the terms by the denominator


3x*8x-23*8x-1=0

Wy multiply elements

24x^2-184x-1=0

a = 24; b = -184; c = -1;
Δ = b2-4ac
Δ = -1842-4·24·(-1)
Δ = 33952
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:

$\sqrt{\Delta}=\sqrt{33952}=\sqrt{16*2122}=\sqrt{16}*\sqrt{2122}=4\sqrt{2122}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-184)-4\sqrt{2122}}{2*24}=\frac{184-4\sqrt{2122}}{48}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-184)+4\sqrt{2122}}{2*24}=\frac{184+4\sqrt{2122}}{48}
$