27+7(2x-6)x=4

Solution for 27+7(2x-6)x=4 equation:

27+7(2x-6)x=4

We move all terms to the left:

27+7(2x-6)x-(4)=0

We add all the numbers together, and all the variables

7(2x-6)x+23=0

We multiply parentheses

14x^2-42x+23=0

a = 14; b = -42; c = +23;
Δ = b2-4ac
Δ = -422-4·14·23
Δ = 476
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:

$\sqrt{\Delta}=\sqrt{476}=\sqrt{4*119}=\sqrt{4}*\sqrt{119}=2\sqrt{119}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-42)-2\sqrt{119}}{2*14}=\frac{42-2\sqrt{119}}{28}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-42)+2\sqrt{119}}{2*14}=\frac{42+2\sqrt{119}}{28}
$