X2-16x-42=0

Solution for X2-16x-42=0 equation:

X2-16X-42=0

We add all the numbers together, and all the variables

X^2-16X-42=0

a = 1; b = -16; c = -42;
Δ = b2-4ac
Δ = -162-4·1·(-42)
Δ = 424
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:

$\sqrt{\Delta}=\sqrt{424}=\sqrt{4*106}=\sqrt{4}*\sqrt{106}=2\sqrt{106}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-2\sqrt{106}}{2*1}=\frac{16-2\sqrt{106}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+2\sqrt{106}}{2*1}=\frac{16+2\sqrt{106}}{2}
$