9x(x-3)=63

Solution for 9x(x-3)=63 equation:

9x(x-3)=63

We move all terms to the left:

9x(x-3)-(63)=0

We multiply parentheses

9x^2-27x-63=0

a = 9; b = -27; c = -63;
Δ = b2-4ac
Δ = -272-4·9·(-63)
Δ = 2997
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:

$\sqrt{\Delta}=\sqrt{2997}=\sqrt{81*37}=\sqrt{81}*\sqrt{37}=9\sqrt{37}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-27)-9\sqrt{37}}{2*9}=\frac{27-9\sqrt{37}}{18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-27)+9\sqrt{37}}{2*9}=\frac{27+9\sqrt{37}}{18}
$