x+x*x=78

Solution for x+x*x=78 equation:

x+x*x=78

We move all terms to the left:

x+x*x-(78)=0

Wy multiply elements

x^2+x-78=0

a = 1; b = 1; c = -78;
Δ = b2-4ac
Δ = 12-4·1·(-78)
Δ = 313
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{313}}{2*1}=\frac{-1-\sqrt{313}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{313}}{2*1}=\frac{-1+\sqrt{313}}{2}
$