x(3x-2)=63

Solution for x(3x-2)=63 equation:

x(3x-2)=63

We move all terms to the left:

x(3x-2)-(63)=0

We multiply parentheses

3x^2-2x-63=0

a = 3; b = -2; c = -63;
Δ = b2-4ac
Δ = -22-4·3·(-63)
Δ = 760
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:

$\sqrt{\Delta}=\sqrt{760}=\sqrt{4*190}=\sqrt{4}*\sqrt{190}=2\sqrt{190}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{190}}{2*3}=\frac{2-2\sqrt{190}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{190}}{2*3}=\frac{2+2\sqrt{190}}{6}
$