6x(2x-7)=27

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

6x(2x-7)=27

We move all terms to the left:

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

We multiply parentheses

12x^2-42x-27=0

a = 12; b = -42; c = -27;
Δ = b2-4ac
Δ = -422-4·12·(-27)
Δ = 3060
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:

$\sqrt{\Delta}=\sqrt{3060}=\sqrt{36*85}=\sqrt{36}*\sqrt{85}=6\sqrt{85}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-42)-6\sqrt{85}}{2*12}=\frac{42-6\sqrt{85}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-42)+6\sqrt{85}}{2*12}=\frac{42+6\sqrt{85}}{24}
$