x^2+30x=52000

Solution for x^2+30x=52000 equation:

x^2+30x=52000

We move all terms to the left:

x^2+30x-(52000)=0

a = 1; b = 30; c = -52000;
Δ = b2-4ac
Δ = 302-4·1·(-52000)
Δ = 208900
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:

$\sqrt{\Delta}=\sqrt{208900}=\sqrt{100*2089}=\sqrt{100}*\sqrt{2089}=10\sqrt{2089}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-10\sqrt{2089}}{2*1}=\frac{-30-10\sqrt{2089}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+10\sqrt{2089}}{2*1}=\frac{-30+10\sqrt{2089}}{2}
$