X^2-16x-45=0

Solution for X^2-16x-45=0 equation:

X^2-16X-45=0

a = 1; b = -16; c = -45;
Δ = b2-4ac
Δ = -162-4·1·(-45)
Δ = 436
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:

$\sqrt{\Delta}=\sqrt{436}=\sqrt{4*109}=\sqrt{4}*\sqrt{109}=2\sqrt{109}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-2\sqrt{109}}{2*1}=\frac{16-2\sqrt{109}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+2\sqrt{109}}{2*1}=\frac{16+2\sqrt{109}}{2}
$