X+x*x=169

Solution for X+x*x=169 equation:

X+X*X=169

We move all terms to the left:

X+X*X-(169)=0

Wy multiply elements

X^2+X-169=0

a = 1; b = 1; c = -169;
Δ = b2-4ac
Δ = 12-4·1·(-169)
Δ = 677
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{677}}{2*1}=\frac{-1-\sqrt{677}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{677}}{2*1}=\frac{-1+\sqrt{677}}{2}
$