x^2-1000x+40=0

Solution for x^2-1000x+40=0 equation:

x^2-1000x+40=0

a = 1; b = -1000; c = +40;
Δ = b2-4ac
Δ = -10002-4·1·40
Δ = 999840
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:

$\sqrt{\Delta}=\sqrt{999840}=\sqrt{16*62490}=\sqrt{16}*\sqrt{62490}=4\sqrt{62490}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1000)-4\sqrt{62490}}{2*1}=\frac{1000-4\sqrt{62490}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1000)+4\sqrt{62490}}{2*1}=\frac{1000+4\sqrt{62490}}{2}
$