16x^2=48x-27

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

16x^2=48x-27

We move all terms to the left:

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

We get rid of parentheses

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