9x(x-7)=81

Solution for 9x(x-7)=81 equation:

9x(x-7)=81

We move all terms to the left:

9x(x-7)-(81)=0

We multiply parentheses

9x^2-63x-81=0

a = 9; b = -63; c = -81;
Δ = b2-4ac
Δ = -632-4·9·(-81)
Δ = 6885
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:

$\sqrt{\Delta}=\sqrt{6885}=\sqrt{81*85}=\sqrt{81}*\sqrt{85}=9\sqrt{85}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-63)-9\sqrt{85}}{2*9}=\frac{63-9\sqrt{85}}{18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-63)+9\sqrt{85}}{2*9}=\frac{63+9\sqrt{85}}{18}
$