0=16x^2+54x+7

Solution for 0=16x^2+54x+7 equation:

0=16x^2+54x+7

We move all terms to the left:

0-(16x^2+54x+7)=0

We add all the numbers together, and all the variables

-(16x^2+54x+7)=0

We get rid of parentheses

-16x^2-54x-7=0

a = -16; b = -54; c = -7;
Δ = b2-4ac
Δ = -542-4·(-16)·(-7)
Δ = 2468
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:

$\sqrt{\Delta}=\sqrt{2468}=\sqrt{4*617}=\sqrt{4}*\sqrt{617}=2\sqrt{617}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-54)-2\sqrt{617}}{2*-16}=\frac{54-2\sqrt{617}}{-32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-54)+2\sqrt{617}}{2*-16}=\frac{54+2\sqrt{617}}{-32}
$