X-1/2y=250

Solution for X-1/2y=250 equation:

X-1/2X=250

We move all terms to the left:

X-1/2X-(250)=0


Domain of the equation: 2X!=0

X!=0/2

X!=0

X∈R


We multiply all the terms by the denominator


X*2X-250*2X-1=0

Wy multiply elements

2X^2-500X-1=0

a = 2; b = -500; c = -1;
Δ = b2-4ac
Δ = -5002-4·2·(-1)
Δ = 250008
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:

$\sqrt{\Delta}=\sqrt{250008}=\sqrt{4*62502}=\sqrt{4}*\sqrt{62502}=2\sqrt{62502}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-500)-2\sqrt{62502}}{2*2}=\frac{500-2\sqrt{62502}}{4}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-500)+2\sqrt{62502}}{2*2}=\frac{500+2\sqrt{62502}}{4}
$