6x^2-18x=14

Solution for 6x^2-18x=14 equation:

6x^2-18x=14

We move all terms to the left:

6x^2-18x-(14)=0

a = 6; b = -18; c = -14;
Δ = b2-4ac
Δ = -182-4·6·(-14)
Δ = 660
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:

$\sqrt{\Delta}=\sqrt{660}=\sqrt{4*165}=\sqrt{4}*\sqrt{165}=2\sqrt{165}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-2\sqrt{165}}{2*6}=\frac{18-2\sqrt{165}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+2\sqrt{165}}{2*6}=\frac{18+2\sqrt{165}}{12}
$