X+1/2x-6=42

Solution for X+1/2x-6=42 equation:

X+1/2X-6=42

We move all terms to the left:

X+1/2X-6-(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

X+1/2X-48=0

We multiply all the terms by the denominator


X*2X-48*2X+1=0

Wy multiply elements

2X^2-96X+1=0

a = 2; b = -96; c = +1;
Δ = b2-4ac
Δ = -962-4·2·1
Δ = 9208
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:

$\sqrt{\Delta}=\sqrt{9208}=\sqrt{4*2302}=\sqrt{4}*\sqrt{2302}=2\sqrt{2302}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-96)-2\sqrt{2302}}{2*2}=\frac{96-2\sqrt{2302}}{4}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-96)+2\sqrt{2302}}{2*2}=\frac{96+2\sqrt{2302}}{4}
$