x^2+16x-23=-5

Solution for x^2+16x-23=-5 equation:

x^2+16x-23=-5

We move all terms to the left:

x^2+16x-23-(-5)=0

We add all the numbers together, and all the variables

x^2+16x-18=0

a = 1; b = 16; c = -18;
Δ = b2-4ac
Δ = 162-4·1·(-18)
Δ = 328
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:

$\sqrt{\Delta}=\sqrt{328}=\sqrt{4*82}=\sqrt{4}*\sqrt{82}=2\sqrt{82}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-2\sqrt{82}}{2*1}=\frac{-16-2\sqrt{82}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+2\sqrt{82}}{2*1}=\frac{-16+2\sqrt{82}}{2}
$