x+x*x=48

Solution for x+x*x=48 equation:

x+x*x=48

We move all terms to the left:

x+x*x-(48)=0

Wy multiply elements

x^2+x-48=0

a = 1; b = 1; c = -48;
Δ = b2-4ac
Δ = 12-4·1·(-48)
Δ = 193
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{193}}{2*1}=\frac{-1-\sqrt{193}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{193}}{2*1}=\frac{-1+\sqrt{193}}{2}
$