(x^2)/3+3x-3000=0

Solution for (x^2)/3+3x-3000=0 equation:

(x^2)/3+3x-3000=0

We multiply all the terms by the denominator


x^2+3x*3-3000*3=0

We add all the numbers together, and all the variables

x^2+3x*3-9000=0

Wy multiply elements

x^2+9x-9000=0

a = 1; b = 9; c = -9000;
Δ = b2-4ac
Δ = 92-4·1·(-9000)
Δ = 36081
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{36081}=\sqrt{9*4009}=\sqrt{9}*\sqrt{4009}=3\sqrt{4009}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-3\sqrt{4009}}{2*1}=\frac{-9-3\sqrt{4009}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+3\sqrt{4009}}{2*1}=\frac{-9+3\sqrt{4009}}{2}
$