X-1/2x=40

Solution for X-1/2x=40 equation:

X-1/2X=40

We move all terms to the left:

X-1/2X-(40)=0


Domain of the equation: 2X!=0

X!=0/2

X!=0

X∈R


We multiply all the terms by the denominator


X*2X-40*2X-1=0

Wy multiply elements

2X^2-80X-1=0

a = 2; b = -80; c = -1;
Δ = b2-4ac
Δ = -802-4·2·(-1)
Δ = 6408
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:

$\sqrt{\Delta}=\sqrt{6408}=\sqrt{36*178}=\sqrt{36}*\sqrt{178}=6\sqrt{178}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-80)-6\sqrt{178}}{2*2}=\frac{80-6\sqrt{178}}{4}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-80)+6\sqrt{178}}{2*2}=\frac{80+6\sqrt{178}}{4}
$