6x^2=8000+x

Solution for 6x^2=8000+x equation:

6x^2=8000+x

We move all terms to the left:

6x^2-(8000+x)=0

We add all the numbers together, and all the variables

6x^2-(x+8000)=0

We get rid of parentheses

6x^2-x-8000=0

We add all the numbers together, and all the variables

6x^2-1x-8000=0

a = 6; b = -1; c = -8000;
Δ = b2-4ac
Δ = -12-4·6·(-8000)
Δ = 192001
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-\sqrt{192001}}{2*6}=\frac{1-\sqrt{192001}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{192001}}{2*6}=\frac{1+\sqrt{192001}}{12}
$