x+1/2x=1400

Solution for x+1/2x=1400 equation:

x+1/2x=1400

We move all terms to the left:

x+1/2x-(1400)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We multiply all the terms by the denominator


x*2x-1400*2x+1=0

Wy multiply elements

2x^2-2800x+1=0

a = 2; b = -2800; c = +1;
Δ = b2-4ac
Δ = -28002-4·2·1
Δ = 7839992
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:

$\sqrt{\Delta}=\sqrt{7839992}=\sqrt{1156*6782}=\sqrt{1156}*\sqrt{6782}=34\sqrt{6782}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2800)-34\sqrt{6782}}{2*2}=\frac{2800-34\sqrt{6782}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2800)+34\sqrt{6782}}{2*2}=\frac{2800+34\sqrt{6782}}{4}
$