8x+x^2=3000

Solution for 8x+x^2=3000 equation:

8x+x^2=3000

We move all terms to the left:

8x+x^2-(3000)=0

a = 1; b = 8; c = -3000;
Δ = b2-4ac
Δ = 82-4·1·(-3000)
Δ = 12064
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:

$\sqrt{\Delta}=\sqrt{12064}=\sqrt{16*754}=\sqrt{16}*\sqrt{754}=4\sqrt{754}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-4\sqrt{754}}{2*1}=\frac{-8-4\sqrt{754}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+4\sqrt{754}}{2*1}=\frac{-8+4\sqrt{754}}{2}
$