27x^2+24-54x=0

Solution for 27x^2+24-54x=0 equation:

27x^2+24-54x=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{36}{54}
=2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-54)+18}{2*27}=\frac{72}{54}
=1+1/3
$