3x(x-20)=x

Solution for 3x(x-20)=x equation:

3x(x-20)=x

We move all terms to the left:

3x(x-20)-(x)=0

We add all the numbers together, and all the variables

-1x+3x(x-20)=0

We multiply parentheses

3x^2-1x-60x=0

We add all the numbers together, and all the variables

3x^2-61x=0

a = 3; b = -61; c = 0;
Δ = b2-4ac
Δ = -612-4·3·0
Δ = 3721
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3721}=61$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-61)-61}{2*3}=\frac{0}{6}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-61)+61}{2*3}=\frac{122}{6}
=20+1/3
$