27x=9x^2

Solution for 27x=9x^2 equation:

27x=9x^2

We move all terms to the left:

27x-(9x^2)=0

determiningTheFunctionDomain
-9x^2+27x=0

a = -9; b = 27; c = 0;
Δ = b2-4ac
Δ = 272-4·(-9)·0
Δ = 729
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{729}=27$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(27)-27}{2*-9}=\frac{-54}{-18}
=+3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(27)+27}{2*-9}=\frac{0}{-18}
=0
$