48x-27=16x^2

Solution for 48x-27=16x^2 equation:

48x-27=16x^2

We move all terms to the left:

48x-27-(16x^2)=0

determiningTheFunctionDomain
-16x^2+48x-27=0

a = -16; b = 48; c = -27;
Δ = b2-4ac
Δ = 482-4·(-16)·(-27)
Δ = 576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{576}=24$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(48)-24}{2*-16}=\frac{-72}{-32}
=2+1/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(48)+24}{2*-16}=\frac{-24}{-32}
=3/4
$