9x(x-7)=63

Solution for 9x(x-7)=63 equation:

9x(x-7)=63

We move all terms to the left:

9x(x-7)-(63)=0

We multiply parentheses

9x^2-63x-63=0

a = 9; b = -63; c = -63;
Δ = b2-4ac
Δ = -632-4·9·(-63)
Δ = 6237
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:

$\sqrt{\Delta}=\sqrt{6237}=\sqrt{81*77}=\sqrt{81}*\sqrt{77}=9\sqrt{77}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-63)-9\sqrt{77}}{2*9}=\frac{63-9\sqrt{77}}{18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-63)+9\sqrt{77}}{2*9}=\frac{63+9\sqrt{77}}{18}
$