x^2+14x=-23

Solution for x^2+14x=-23 equation:

x^2+14x=-23

We move all terms to the left:

x^2+14x-(-23)=0

We add all the numbers together, and all the variables

x^2+14x+23=0

a = 1; b = 14; c = +23;
Δ = b2-4ac
Δ = 142-4·1·23
Δ = 104
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:

$\sqrt{\Delta}=\sqrt{104}=\sqrt{4*26}=\sqrt{4}*\sqrt{26}=2\sqrt{26}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-2\sqrt{26}}{2*1}=\frac{-14-2\sqrt{26}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+2\sqrt{26}}{2*1}=\frac{-14+2\sqrt{26}}{2}
$