0=4x^2-27x-54

Solution for 0=4x^2-27x-54 equation:

0=4x^2-27x-54

We move all terms to the left:

0-(4x^2-27x-54)=0

We add all the numbers together, and all the variables

-(4x^2-27x-54)=0

We get rid of parentheses

-4x^2+27x+54=0

a = -4; b = 27; c = +54;
Δ = b2-4ac
Δ = 272-4·(-4)·54
Δ = 1593
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:

$\sqrt{\Delta}=\sqrt{1593}=\sqrt{9*177}=\sqrt{9}*\sqrt{177}=3\sqrt{177}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(27)-3\sqrt{177}}{2*-4}=\frac{-27-3\sqrt{177}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(27)+3\sqrt{177}}{2*-4}=\frac{-27+3\sqrt{177}}{-8}
$