x^2+2x=54000

Solution for x^2+2x=54000 equation:

x^2+2x=54000

We move all terms to the left:

x^2+2x-(54000)=0

a = 1; b = 2; c = -54000;
Δ = b2-4ac
Δ = 22-4·1·(-54000)
Δ = 216004
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:

$\sqrt{\Delta}=\sqrt{216004}=\sqrt{4*54001}=\sqrt{4}*\sqrt{54001}=2\sqrt{54001}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{54001}}{2*1}=\frac{-2-2\sqrt{54001}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{54001}}{2*1}=\frac{-2+2\sqrt{54001}}{2}
$