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

Solution for 2x+3x(x-1)=27 equation:

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

We move all terms to the left:

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

We multiply parentheses

3x^2+2x-3x-27=0

We add all the numbers together, and all the variables

3x^2-1x-27=0

a = 3; b = -1; c = -27;
Δ = b2-4ac
Δ = -12-4·3·(-27)
Δ = 325
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{325}=\sqrt{25*13}=\sqrt{25}*\sqrt{13}=5\sqrt{13}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-5\sqrt{13}}{2*3}=\frac{1-5\sqrt{13}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+5\sqrt{13}}{2*3}=\frac{1+5\sqrt{13}}{6}
$