3x(x-9)=5

Solution for 3x(x-9)=5 equation:

3x(x-9)=5

We move all terms to the left:

3x(x-9)-(5)=0

We multiply parentheses

3x^2-27x-5=0

a = 3; b = -27; c = -5;
Δ = b2-4ac
Δ = -272-4·3·(-5)
Δ = 789
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-27)-\sqrt{789}}{2*3}=\frac{27-\sqrt{789}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-27)+\sqrt{789}}{2*3}=\frac{27+\sqrt{789}}{6}
$