(5r+9)(r+6)=0

Solution for (5r+9)(r+6)=0 equation:

(5r+9)(r+6)=0

We multiply parentheses ..

(+5r^2+30r+9r+54)=0

We get rid of parentheses

5r^2+30r+9r+54=0

We add all the numbers together, and all the variables

5r^2+39r+54=0

a = 5; b = 39; c = +54;
Δ = b2-4ac
Δ = 392-4·5·54
Δ = 441
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{441}=21$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(39)-21}{2*5}=\frac{-60}{10}
=-6
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(39)+21}{2*5}=\frac{-18}{10}
=-1+4/5
$