0=4x^2-54x+48

Solution for 0=4x^2-54x+48 equation:

0=4x^2-54x+48

We move all terms to the left:

0-(4x^2-54x+48)=0

We add all the numbers together, and all the variables

-(4x^2-54x+48)=0

We get rid of parentheses

-4x^2+54x-48=0

a = -4; b = 54; c = -48;
Δ = b2-4ac
Δ = 542-4·(-4)·(-48)
Δ = 2148
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:

$\sqrt{\Delta}=\sqrt{2148}=\sqrt{4*537}=\sqrt{4}*\sqrt{537}=2\sqrt{537}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(54)-2\sqrt{537}}{2*-4}=\frac{-54-2\sqrt{537}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(54)+2\sqrt{537}}{2*-4}=\frac{-54+2\sqrt{537}}{-8}
$