x+x^2+x+x^2=84

Solution for x+x^2+x+x^2=84 equation:

x+x^2+x+x^2=84

We move all terms to the left:

x+x^2+x+x^2-(84)=0

We add all the numbers together, and all the variables

2x^2+2x-84=0

a = 2; b = 2; c = -84;
Δ = b2-4ac
Δ = 22-4·2·(-84)
Δ = 676
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{676}=26$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-26}{2*2}=\frac{-28}{4}
=-7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+26}{2*2}=\frac{24}{4}
=6
$