600/x=1+x

Solution for 600/x=1+x equation:

600/x=1+x

We move all terms to the left:

600/x-(1+x)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

600/x-(x+1)=0

We get rid of parentheses

600/x-x-1=0

We multiply all the terms by the denominator


-x*x-1*x+600=0

We add all the numbers together, and all the variables

-1x-x*x+600=0

Wy multiply elements

-1x^2-1x+600=0

a = -1; b = -1; c = +600;
Δ = b2-4ac
Δ = -12-4·(-1)·600
Δ = 2401
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2401}=49$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-49}{2*-1}=\frac{-48}{-2}
=+24
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+49}{2*-1}=\frac{50}{-2}
=-25
$