54x=27x^2+24

Solution for 54x=27x^2+24 equation:

54x=27x^2+24

We move all terms to the left:

54x-(27x^2+24)=0

We get rid of parentheses

-27x^2+54x-24=0

a = -27; b = 54; c = -24;
Δ = b2-4ac
Δ = 542-4·(-27)·(-24)
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(54)-18}{2*-27}=\frac{-72}{-54}
=1+1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(54)+18}{2*-27}=\frac{-36}{-54}
=2/3
$