3x-8-1/2x=42

Solution for 3x-8-1/2x=42 equation:

3x-8-1/2x=42

We move all terms to the left:

3x-8-1/2x-(42)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

3x-1/2x-50=0

We multiply all the terms by the denominator


3x*2x-50*2x-1=0

Wy multiply elements

6x^2-100x-1=0

a = 6; b = -100; c = -1;
Δ = b2-4ac
Δ = -1002-4·6·(-1)
Δ = 10024
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:

$\sqrt{\Delta}=\sqrt{10024}=\sqrt{4*2506}=\sqrt{4}*\sqrt{2506}=2\sqrt{2506}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-100)-2\sqrt{2506}}{2*6}=\frac{100-2\sqrt{2506}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-100)+2\sqrt{2506}}{2*6}=\frac{100+2\sqrt{2506}}{12}
$