x^2+45x+12=-188

Solution for x^2+45x+12=-188 equation:

x^2+45x+12=-188

We move all terms to the left:

x^2+45x+12-(-188)=0

We add all the numbers together, and all the variables

x^2+45x+200=0

a = 1; b = 45; c = +200;
Δ = b2-4ac
Δ = 452-4·1·200
Δ = 1225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1225}=35$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(45)-35}{2*1}=\frac{-80}{2}
=-40
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(45)+35}{2*1}=\frac{-10}{2}
=-5
$