x2-10x-1600=0

Solution for x2-10x-1600=0 equation:

X2-10X-1600=0

We add all the numbers together, and all the variables

X^2-10X-1600=0

a = 1; b = -10; c = -1600;
Δ = b2-4ac
Δ = -102-4·1·(-1600)
Δ = 6500
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:

$\sqrt{\Delta}=\sqrt{6500}=\sqrt{100*65}=\sqrt{100}*\sqrt{65}=10\sqrt{65}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-10\sqrt{65}}{2*1}=\frac{10-10\sqrt{65}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+10\sqrt{65}}{2*1}=\frac{10+10\sqrt{65}}{2}
$