0=5x^2-6x-54

Solution for 0=5x^2-6x-54 equation:

0=5x^2-6x-54

We move all terms to the left:

0-(5x^2-6x-54)=0

We add all the numbers together, and all the variables

-(5x^2-6x-54)=0

We get rid of parentheses

-5x^2+6x+54=0

a = -5; b = 6; c = +54;
Δ = b2-4ac
Δ = 62-4·(-5)·54
Δ = 1116
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:

$\sqrt{\Delta}=\sqrt{1116}=\sqrt{36*31}=\sqrt{36}*\sqrt{31}=6\sqrt{31}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-6\sqrt{31}}{2*-5}=\frac{-6-6\sqrt{31}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+6\sqrt{31}}{2*-5}=\frac{-6+6\sqrt{31}}{-10}
$