x(9x-27)=972

Solution for x(9x-27)=972 equation:

x(9x-27)=972

We move all terms to the left:

x(9x-27)-(972)=0

We multiply parentheses

9x^2-27x-972=0

a = 9; b = -27; c = -972;
Δ = b2-4ac
Δ = -272-4·9·(-972)
Δ = 35721
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{35721}=189$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-27)-189}{2*9}=\frac{-162}{18}
=-9
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-27)+189}{2*9}=\frac{216}{18}
=12
$