635x+x^2-42000=0

Solution for 635x+x^2-42000=0 equation:

635x+x^2-42000=0

a = 1; b = 635; c = -42000;
Δ = b2-4ac
Δ = 6352-4·1·(-42000)
Δ = 571225
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:

$\sqrt{\Delta}=\sqrt{571225}=\sqrt{25*22849}=\sqrt{25}*\sqrt{22849}=5\sqrt{22849}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(635)-5\sqrt{22849}}{2*1}=\frac{-635-5\sqrt{22849}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(635)+5\sqrt{22849}}{2*1}=\frac{-635+5\sqrt{22849}}{2}
$