x(3x+5000)=3x

Solution for x(3x+5000)=3x equation:

x(3x+5000)=3x

We move all terms to the left:

x(3x+5000)-(3x)=0

We add all the numbers together, and all the variables

-3x+x(3x+5000)=0

We multiply parentheses

3x^2-3x+5000x=0

We add all the numbers together, and all the variables

3x^2+4997x=0

a = 3; b = 4997; c = 0;
Δ = b2-4ac
Δ = 49972-4·3·0
Δ = 24970009
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{24970009}=4997$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4997)-4997}{2*3}=\frac{-9994}{6}
=-1665+2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4997)+4997}{2*3}=\frac{0}{6}
=0
$