24x^2-27x=2

Solution for 24x^2-27x=2 equation:

24x^2-27x=2

We move all terms to the left:

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

a = 24; b = -27; c = -2;
Δ = b2-4ac
Δ = -272-4·24·(-2)
Δ = 921
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{921}}{2*24}=\frac{27-\sqrt{921}}{48}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-27)+\sqrt{921}}{2*24}=\frac{27+\sqrt{921}}{48}
$