x2-34x-10000=0

Solution for x2-34x-10000=0 equation:

x2-34x-10000=0

We add all the numbers together, and all the variables

x^2-34x-10000=0

a = 1; b = -34; c = -10000;
Δ = b2-4ac
Δ = -342-4·1·(-10000)
Δ = 41156
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:

$\sqrt{\Delta}=\sqrt{41156}=\sqrt{4*10289}=\sqrt{4}*\sqrt{10289}=2\sqrt{10289}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-34)-2\sqrt{10289}}{2*1}=\frac{34-2\sqrt{10289}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-34)+2\sqrt{10289}}{2*1}=\frac{34+2\sqrt{10289}}{2}
$