x+x^2=2.6667

Solution for x+x^2=2.6667 equation:

x+x^2=2.6667

We move all terms to the left:

x+x^2-(2.6667)=0

We add all the numbers together, and all the variables

x^2+x-2.6667=0

a = 1; b = 1; c = -2.6667;
Δ = b2-4ac
Δ = 12-4·1·(-2.6667)
Δ = 11.6668
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{11.6668}}{2*1}=\frac{-1-\sqrt{11.6668}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{11.6668}}{2*1}=\frac{-1+\sqrt{11.6668}}{2}
$