X^2-90x-2000=0

Solution for X^2-90x-2000=0 equation:

X^2-90X-2000=0

a = 1; b = -90; c = -2000;
Δ = b2-4ac
Δ = -902-4·1·(-2000)
Δ = 16100
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:

$\sqrt{\Delta}=\sqrt{16100}=\sqrt{100*161}=\sqrt{100}*\sqrt{161}=10\sqrt{161}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-90)-10\sqrt{161}}{2*1}=\frac{90-10\sqrt{161}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-90)+10\sqrt{161}}{2*1}=\frac{90+10\sqrt{161}}{2}
$