39x-3x^2=54

Solution for 39x-3x^2=54 equation:

39x-3x^2=54

We move all terms to the left:

39x-3x^2-(54)=0

a = -3; b = 39; c = -54;
Δ = b2-4ac
Δ = 392-4·(-3)·(-54)
Δ = 873
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:

$\sqrt{\Delta}=\sqrt{873}=\sqrt{9*97}=\sqrt{9}*\sqrt{97}=3\sqrt{97}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(39)-3\sqrt{97}}{2*-3}=\frac{-39-3\sqrt{97}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(39)+3\sqrt{97}}{2*-3}=\frac{-39+3\sqrt{97}}{-6}
$