800/x=60-x

Solution for 800/x=60-x equation:

800/x=60-x

We move all terms to the left:

800/x-(60-x)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

800/x-(-1x+60)=0

We get rid of parentheses

800/x+1x-60=0

We multiply all the terms by the denominator


1x*x-60*x+800=0

We add all the numbers together, and all the variables

-60x+1x*x+800=0

Wy multiply elements

x^2-60x+800=0

a = 1; b = -60; c = +800;
Δ = b2-4ac
Δ = -602-4·1·800
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-60)-20}{2*1}=\frac{40}{2}
=20
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-60)+20}{2*1}=\frac{80}{2}
=40
$