x+300+1/2x=1500

Solution for x+300+1/2x=1500 equation:

x+300+1/2x=1500

We move all terms to the left:

x+300+1/2x-(1500)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

x+1/2x-1200=0

We multiply all the terms by the denominator


x*2x-1200*2x+1=0

Wy multiply elements

2x^2-2400x+1=0

a = 2; b = -2400; c = +1;
Δ = b2-4ac
Δ = -24002-4·2·1
Δ = 5759992
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:

$\sqrt{\Delta}=\sqrt{5759992}=\sqrt{4*1439998}=\sqrt{4}*\sqrt{1439998}=2\sqrt{1439998}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2400)-2\sqrt{1439998}}{2*2}=\frac{2400-2\sqrt{1439998}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2400)+2\sqrt{1439998}}{2*2}=\frac{2400+2\sqrt{1439998}}{4}
$