x2-280x-34000=0

Solution for x2-280x-34000=0 equation:

x2-280x-34000=0

We add all the numbers together, and all the variables

x^2-280x-34000=0

a = 1; b = -280; c = -34000;
Δ = b2-4ac
Δ = -2802-4·1·(-34000)
Δ = 214400
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:

$\sqrt{\Delta}=\sqrt{214400}=\sqrt{1600*134}=\sqrt{1600}*\sqrt{134}=40\sqrt{134}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-280)-40\sqrt{134}}{2*1}=\frac{280-40\sqrt{134}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-280)+40\sqrt{134}}{2*1}=\frac{280+40\sqrt{134}}{2}
$