3x(62-x)=x

Solution for 3x(62-x)=x equation:

3x(62-x)=x

We move all terms to the left:

3x(62-x)-(x)=0

We add all the numbers together, and all the variables

3x(-1x+62)-x=0

We add all the numbers together, and all the variables

-1x+3x(-1x+62)=0

We multiply parentheses

-3x^2-1x+186x=0

We add all the numbers together, and all the variables

-3x^2+185x=0

a = -3; b = 185; c = 0;
Δ = b2-4ac
Δ = 1852-4·(-3)·0
Δ = 34225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{34225}=185$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(185)-185}{2*-3}=\frac{-370}{-6}
=61+2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(185)+185}{2*-3}=\frac{0}{-6}
=0
$