X+1/2x=1650

Solution for X+1/2x=1650 equation:

X+1/2X=1650

We move all terms to the left:

X+1/2X-(1650)=0


Domain of the equation: 2X!=0

X!=0/2

X!=0

X∈R


We multiply all the terms by the denominator


X*2X-1650*2X+1=0

Wy multiply elements

2X^2-3300X+1=0

a = 2; b = -3300; c = +1;
Δ = b2-4ac
Δ = -33002-4·2·1
Δ = 10889992
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:

$\sqrt{\Delta}=\sqrt{10889992}=\sqrt{4*2722498}=\sqrt{4}*\sqrt{2722498}=2\sqrt{2722498}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3300)-2\sqrt{2722498}}{2*2}=\frac{3300-2\sqrt{2722498}}{4}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3300)+2\sqrt{2722498}}{2*2}=\frac{3300+2\sqrt{2722498}}{4}
$