3(x-2)x=14

Solution for 3(x-2)x=14 equation:

3(x-2)x=14

We move all terms to the left:

3(x-2)x-(14)=0

We multiply parentheses

3x^2-6x-14=0

a = 3; b = -6; c = -14;
Δ = b2-4ac
Δ = -62-4·3·(-14)
Δ = 204
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:

$\sqrt{\Delta}=\sqrt{204}=\sqrt{4*51}=\sqrt{4}*\sqrt{51}=2\sqrt{51}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{51}}{2*3}=\frac{6-2\sqrt{51}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{51}}{2*3}=\frac{6+2\sqrt{51}}{6}
$