X^2-16x+5=-9

Solution for X^2-16x+5=-9 equation:

X^2-16X+5=-9

We move all terms to the left:

X^2-16X+5-(-9)=0

We add all the numbers together, and all the variables

X^2-16X+14=0

a = 1; b = -16; c = +14;
Δ = b2-4ac
Δ = -162-4·1·14
Δ = 200
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:

$\sqrt{\Delta}=\sqrt{200}=\sqrt{100*2}=\sqrt{100}*\sqrt{2}=10\sqrt{2}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-10\sqrt{2}}{2*1}=\frac{16-10\sqrt{2}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+10\sqrt{2}}{2*1}=\frac{16+10\sqrt{2}}{2}
$