(750000/x)+.5x=500000

Solution for (750000/x)+.5x=500000 equation:

(750000/x)+.5x=500000

We move all terms to the left:

(750000/x)+.5x-(500000)=0


Domain of the equation: x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

(+750000/x)+.5x-500000=0

We add all the numbers together, and all the variables

.5x+(+750000/x)-500000=0

We get rid of parentheses

.5x+750000/x-500000=0

We multiply all the terms by the denominator


(.5x)*x-500000*x+750000=0

We add all the numbers together, and all the variables

(+.5x)*x-500000*x+750000=0

We add all the numbers together, and all the variables

-500000x+(+.5x)*x+750000=0

We multiply parentheses

x^2-500000x+750000=0

a = 1; b = -500000; c = +750000;
Δ = b2-4ac
Δ = -5000002-4·1·750000
Δ = 249997000000
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:

$\sqrt{\Delta}=\sqrt{249997000000}=\sqrt{1000000*249997}=\sqrt{1000000}*\sqrt{249997}=1000\sqrt{249997}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-500000)-1000\sqrt{249997}}{2*1}=\frac{500000-1000\sqrt{249997}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-500000)+1000\sqrt{249997}}{2*1}=\frac{500000+1000\sqrt{249997}}{2}
$