x2+26x+92=-74

Solution for x2+26x+92=-74 equation:

x2+26x+92=-74

We move all terms to the left:

x2+26x+92-(-74)=0

We add all the numbers together, and all the variables

x^2+26x+166=0

a = 1; b = 26; c = +166;
Δ = b2-4ac
Δ = 262-4·1·166
Δ = 12
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:

$\sqrt{\Delta}=\sqrt{12}=\sqrt{4*3}=\sqrt{4}*\sqrt{3}=2\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(26)-2\sqrt{3}}{2*1}=\frac{-26-2\sqrt{3}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(26)+2\sqrt{3}}{2*1}=\frac{-26+2\sqrt{3}}{2}
$