X+2x^2=27

Solution for X+2x^2=27 equation:

X+2X^2=27

We move all terms to the left:

X+2X^2-(27)=0

a = 2; b = 1; c = -27;
Δ = b2-4ac
Δ = 12-4·2·(-27)
Δ = 217
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{217}}{2*2}=\frac{-1-\sqrt{217}}{4}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{217}}{2*2}=\frac{-1+\sqrt{217}}{4}
$