X+1/2x=42

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

X+1/2X=42

We move all terms to the left:

X+1/2X-(42)=0


Domain of the equation: 2X!=0

X!=0/2

X!=0

X∈R


We multiply all the terms by the denominator


X*2X-42*2X+1=0

Wy multiply elements

2X^2-84X+1=0

a = 2; b = -84; c = +1;
Δ = b2-4ac
Δ = -842-4·2·1
Δ = 7048
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:

$\sqrt{\Delta}=\sqrt{7048}=\sqrt{4*1762}=\sqrt{4}*\sqrt{1762}=2\sqrt{1762}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-84)-2\sqrt{1762}}{2*2}=\frac{84-2\sqrt{1762}}{4}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-84)+2\sqrt{1762}}{2*2}=\frac{84+2\sqrt{1762}}{4}
$