6x^2-12x-9=28

Solution for 6x^2-12x-9=28 equation:

6x^2-12x-9=28

We move all terms to the left:

6x^2-12x-9-(28)=0

We add all the numbers together, and all the variables

6x^2-12x-37=0

a = 6; b = -12; c = -37;
Δ = b2-4ac
Δ = -122-4·6·(-37)
Δ = 1032
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:

$\sqrt{\Delta}=\sqrt{1032}=\sqrt{4*258}=\sqrt{4}*\sqrt{258}=2\sqrt{258}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-2\sqrt{258}}{2*6}=\frac{12-2\sqrt{258}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+2\sqrt{258}}{2*6}=\frac{12+2\sqrt{258}}{12}
$