x2+2x+6=294

Solution for x2+2x+6=294 equation:

x2+2x+6=294

We move all terms to the left:

x2+2x+6-(294)=0

We add all the numbers together, and all the variables

x^2+2x-288=0

a = 1; b = 2; c = -288;
Δ = b2-4ac
Δ = 22-4·1·(-288)
Δ = 1156
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1156}=34$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-34}{2*1}=\frac{-36}{2}
=-18
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+34}{2*1}=\frac{32}{2}
=16
$