X+3x2=84

Solution for X+3x2=84 equation:

X+3X^2=84

We move all terms to the left:

X+3X^2-(84)=0

a = 3; b = 1; c = -84;
Δ = b2-4ac
Δ = 12-4·3·(-84)
Δ = 1009
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{1009}}{2*3}=\frac{-1-\sqrt{1009}}{6}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{1009}}{2*3}=\frac{-1+\sqrt{1009}}{6}
$