40x+x^2=6000

Solution for 40x+x^2=6000 equation:

40x+x^2=6000

We move all terms to the left:

40x+x^2-(6000)=0

a = 1; b = 40; c = -6000;
Δ = b2-4ac
Δ = 402-4·1·(-6000)
Δ = 25600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25600}=160$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(40)-160}{2*1}=\frac{-200}{2}
=-100
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(40)+160}{2*1}=\frac{120}{2}
=60
$