20x/x=x+1

Solution for 20x/x=x+1 equation:

20x/x=x+1

We move all terms to the left:

20x/x-(x+1)=0


Domain of the equation: x!=0

x∈R


We get rid of parentheses

20x/x-x-1=0

We multiply all the terms by the denominator


20x-x*x-1*x=0

We add all the numbers together, and all the variables

19x-x*x=0

Wy multiply elements

-1x^2+19x=0

a = -1; b = 19; c = 0;
Δ = b2-4ac
Δ = 192-4·(-1)·0
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(19)-19}{2*-1}=\frac{-38}{-2}
=+19
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(19)+19}{2*-1}=\frac{0}{-2}
=0
$