x+(x^2)=378

Solution for x+(x^2)=378 equation:

x+(x^2)=378

We move all terms to the left:

x+(x^2)-(378)=0

determiningTheFunctionDomain
x^2+x-378=0

a = 1; b = 1; c = -378;
Δ = b2-4ac
Δ = 12-4·1·(-378)
Δ = 1513
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{-(1)-\sqrt{1513}}{2*1}=\frac{-1-\sqrt{1513}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{1513}}{2*1}=\frac{-1+\sqrt{1513}}{2}
$