r*r-3r-54=0

Solution for r*r-3r-54=0 equation:

r*r-3r-54=0

We add all the numbers together, and all the variables

-3r+r*r-54=0

Wy multiply elements

r^2-3r-54=0

a = 1; b = -3; c = -54;
Δ = b2-4ac
Δ = -32-4·1·(-54)
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-15}{2*1}=\frac{-12}{2}
=-6
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+15}{2*1}=\frac{18}{2}
=9
$