16x^2+2=48x-27

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

16x^2+2=48x-27

We move all terms to the left:

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

16x^2-48x+29=0

a = 16; b = -48; c = +29;
Δ = b2-4ac
Δ = -482-4·16·29
Δ = 448
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{448}=\sqrt{64*7}=\sqrt{64}*\sqrt{7}=8\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-48)-8\sqrt{7}}{2*16}=\frac{48-8\sqrt{7}}{32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-48)+8\sqrt{7}}{2*16}=\frac{48+8\sqrt{7}}{32}
$