X+1/2x=1750

Solution for X+1/2x=1750 equation:

X+1/2X=1750

We move all terms to the left:

X+1/2X-(1750)=0


Domain of the equation: 2X!=0

X!=0/2

X!=0

X∈R


We multiply all the terms by the denominator


X*2X-1750*2X+1=0

Wy multiply elements

2X^2-3500X+1=0

a = 2; b = -3500; c = +1;
Δ = b2-4ac
Δ = -35002-4·2·1
Δ = 12249992
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:

$\sqrt{\Delta}=\sqrt{12249992}=\sqrt{4*3062498}=\sqrt{4}*\sqrt{3062498}=2\sqrt{3062498}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3500)-2\sqrt{3062498}}{2*2}=\frac{3500-2\sqrt{3062498}}{4}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3500)+2\sqrt{3062498}}{2*2}=\frac{3500+2\sqrt{3062498}}{4}
$