24x^2-15=54x

Solution for 24x^2-15=54x equation:

24x^2-15=54x

We move all terms to the left:

24x^2-15-(54x)=0

a = 24; b = -54; c = -15;
Δ = b2-4ac
Δ = -542-4·24·(-15)
Δ = 4356
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4356}=66$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-54)-66}{2*24}=\frac{-12}{48}
=-1/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-54)+66}{2*24}=\frac{120}{48}
=2+1/2
$