X^2+27x+176=12

Solution for X^2+27x+176=12 equation:

X^2+27X+176=12

We move all terms to the left:

X^2+27X+176-(12)=0

We add all the numbers together, and all the variables

X^2+27X+164=0

a = 1; b = 27; c = +164;
Δ = b2-4ac
Δ = 272-4·1·164
Δ = 73
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(27)-\sqrt{73}}{2*1}=\frac{-27-\sqrt{73}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(27)+\sqrt{73}}{2*1}=\frac{-27+\sqrt{73}}{2}
$