3x2+x+1=27

Solution for 3x2+x+1=27 equation:

3x^2+x+1=27

We move all terms to the left:

3x^2+x+1-(27)=0

We add all the numbers together, and all the variables

3x^2+x-26=0

a = 3; b = 1; c = -26;
Δ = b2-4ac
Δ = 12-4·3·(-26)
Δ = 313
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{313}}{2*3}=\frac{-1-\sqrt{313}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{313}}{2*3}=\frac{-1+\sqrt{313}}{6}
$