3x(x-2)=14641

Solution for 3x(x-2)=14641 equation:

3x(x-2)=14641

We move all terms to the left:

3x(x-2)-(14641)=0

We multiply parentheses

3x^2-6x-14641=0

a = 3; b = -6; c = -14641;
Δ = b2-4ac
Δ = -62-4·3·(-14641)
Δ = 175728
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:

$\sqrt{\Delta}=\sqrt{175728}=\sqrt{16*10983}=\sqrt{16}*\sqrt{10983}=4\sqrt{10983}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-4\sqrt{10983}}{2*3}=\frac{6-4\sqrt{10983}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+4\sqrt{10983}}{2*3}=\frac{6+4\sqrt{10983}}{6}
$