x2+x=380

Solution for x2+x=380 equation:

x2+x=380

We move all terms to the left:

x2+x-(380)=0

We add all the numbers together, and all the variables

x^2+x-380=0

a = 1; b = 1; c = -380;
Δ = b2-4ac
Δ = 12-4·1·(-380)
Δ = 1521
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1521}=39$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-39}{2*1}=\frac{-40}{2}
=-20
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+39}{2*1}=\frac{38}{2}
=19
$