-3x(2x-3)+x+4=-27

Solution for -3x(2x-3)+x+4=-27 equation:

-3x(2x-3)+x+4=-27

We move all terms to the left:

-3x(2x-3)+x+4-(-27)=0

We add all the numbers together, and all the variables

x-3x(2x-3)+31=0

We multiply parentheses

-6x^2+x+9x+31=0

We add all the numbers together, and all the variables

-6x^2+10x+31=0

a = -6; b = 10; c = +31;
Δ = b2-4ac
Δ = 102-4·(-6)·31
Δ = 844
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:

$\sqrt{\Delta}=\sqrt{844}=\sqrt{4*211}=\sqrt{4}*\sqrt{211}=2\sqrt{211}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{211}}{2*-6}=\frac{-10-2\sqrt{211}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{211}}{2*-6}=\frac{-10+2\sqrt{211}}{-12}
$