X2+16x+46=0

Solution for X2+16x+46=0 equation:

X2+16X+46=0

We add all the numbers together, and all the variables

X^2+16X+46=0

a = 1; b = 16; c = +46;
Δ = b2-4ac
Δ = 162-4·1·46
Δ = 72
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:

$\sqrt{\Delta}=\sqrt{72}=\sqrt{36*2}=\sqrt{36}*\sqrt{2}=6\sqrt{2}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-6\sqrt{2}}{2*1}=\frac{-16-6\sqrt{2}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+6\sqrt{2}}{2*1}=\frac{-16+6\sqrt{2}}{2}
$