X^2-160x-1000=0

Solution for X^2-160x-1000=0 equation:

X^2-160X-1000=0

a = 1; b = -160; c = -1000;
Δ = b2-4ac
Δ = -1602-4·1·(-1000)
Δ = 29600
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:

$\sqrt{\Delta}=\sqrt{29600}=\sqrt{400*74}=\sqrt{400}*\sqrt{74}=20\sqrt{74}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-160)-20\sqrt{74}}{2*1}=\frac{160-20\sqrt{74}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-160)+20\sqrt{74}}{2*1}=\frac{160+20\sqrt{74}}{2}
$