12x2-27x=-6

Solution for 12x2-27x=-6 equation:

12x^2-27x=-6

We move all terms to the left:

12x^2-27x-(-6)=0

We add all the numbers together, and all the variables

12x^2-27x+6=0

a = 12; b = -27; c = +6;
Δ = b2-4ac
Δ = -272-4·12·6
Δ = 441
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{441}=21$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-27)-21}{2*12}=\frac{6}{24}
=1/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-27)+21}{2*12}=\frac{48}{24}
=2
$