6x^2+18x-166x=2

Solution for 6x^2+18x-166x=2 equation:

6x^2+18x-166x=2

We move all terms to the left:

6x^2+18x-166x-(2)=0

We add all the numbers together, and all the variables

6x^2-148x-2=0

a = 6; b = -148; c = -2;
Δ = b2-4ac
Δ = -1482-4·6·(-2)
Δ = 21952
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:

$\sqrt{\Delta}=\sqrt{21952}=\sqrt{3136*7}=\sqrt{3136}*\sqrt{7}=56\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-148)-56\sqrt{7}}{2*6}=\frac{148-56\sqrt{7}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-148)+56\sqrt{7}}{2*6}=\frac{148+56\sqrt{7}}{12}
$