x2+x=306

Solution for x2+x=306 equation:

x2+x=306

We move all terms to the left:

x2+x-(306)=0

We add all the numbers together, and all the variables

x^2+x-306=0

a = 1; b = 1; c = -306;
Δ = b2-4ac
Δ = 12-4·1·(-306)
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{-(1)-35}{2*1}=\frac{-36}{2}
=-18
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+35}{2*1}=\frac{34}{2}
=17
$