x^2+27x+176=36

Solution for x^2+27x+176=36 equation:

x^2+27x+176=36

We move all terms to the left:

x^2+27x+176-(36)=0

We add all the numbers together, and all the variables

x^2+27x+140=0

a = 1; b = 27; c = +140;
Δ = b2-4ac
Δ = 272-4·1·140
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(27)-13}{2*1}=\frac{-40}{2}
=-20
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(27)+13}{2*1}=\frac{-14}{2}
=-7
$