80/x=x-20

Solution for 80/x=x-20 equation:

80/x=x-20

We move all terms to the left:

80/x-(x-20)=0


Domain of the equation: x!=0

x∈R


We get rid of parentheses

80/x-x+20=0

We multiply all the terms by the denominator


-x*x+20*x+80=0

We add all the numbers together, and all the variables

20x-x*x+80=0

Wy multiply elements

-1x^2+20x+80=0

a = -1; b = 20; c = +80;
Δ = b2-4ac
Δ = 202-4·(-1)·80
Δ = 720
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:

$\sqrt{\Delta}=\sqrt{720}=\sqrt{144*5}=\sqrt{144}*\sqrt{5}=12\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-12\sqrt{5}}{2*-1}=\frac{-20-12\sqrt{5}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+12\sqrt{5}}{2*-1}=\frac{-20+12\sqrt{5}}{-2}
$