X+1/2x=300

Solution for X+1/2x=300 equation:

X+1/2X=300

We move all terms to the left:

X+1/2X-(300)=0


Domain of the equation: 2X!=0

X!=0/2

X!=0

X∈R


We multiply all the terms by the denominator


X*2X-300*2X+1=0

Wy multiply elements

2X^2-600X+1=0

a = 2; b = -600; c = +1;
Δ = b2-4ac
Δ = -6002-4·2·1
Δ = 359992
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:

$\sqrt{\Delta}=\sqrt{359992}=\sqrt{4*89998}=\sqrt{4}*\sqrt{89998}=2\sqrt{89998}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-600)-2\sqrt{89998}}{2*2}=\frac{600-2\sqrt{89998}}{4}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-600)+2\sqrt{89998}}{2*2}=\frac{600+2\sqrt{89998}}{4}
$