X-1/2x=19

Solution for X-1/2x=19 equation:

X-1/2X=19

We move all terms to the left:

X-1/2X-(19)=0


Domain of the equation: 2X!=0

X!=0/2

X!=0

X∈R


We multiply all the terms by the denominator


X*2X-19*2X-1=0

Wy multiply elements

2X^2-38X-1=0

a = 2; b = -38; c = -1;
Δ = b2-4ac
Δ = -382-4·2·(-1)
Δ = 1452
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:

$\sqrt{\Delta}=\sqrt{1452}=\sqrt{484*3}=\sqrt{484}*\sqrt{3}=22\sqrt{3}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-38)-22\sqrt{3}}{2*2}=\frac{38-22\sqrt{3}}{4}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-38)+22\sqrt{3}}{2*2}=\frac{38+22\sqrt{3}}{4}
$