x(3x+5000)=3x

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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 $

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