p^2+26p=-43

Solution for p^2+26p=-43 equation:

p^2+26p=-43

We move all terms to the left:

p^2+26p-(-43)=0

We add all the numbers together, and all the variables

p^2+26p+43=0

a = 1; b = 26; c = +43;
Δ = b2-4ac
Δ = 262-4·1·43
Δ = 504
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{504}=\sqrt{36*14}=\sqrt{36}*\sqrt{14}=6\sqrt{14}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(26)-6\sqrt{14}}{2*1}=\frac{-26-6\sqrt{14}}{2}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(26)+6\sqrt{14}}{2*1}=\frac{-26+6\sqrt{14}}{2}
$