5r(r+6)=5

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

5r(r+6)=5

We move all terms to the left:

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

We multiply parentheses

5r^2+30r-5=0

a = 5; b = 30; c = -5;
Δ = b2-4ac
Δ = 302-4·5·(-5)
Δ = 1000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1000}=\sqrt{100*10}=\sqrt{100}*\sqrt{10}=10\sqrt{10}$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-10\sqrt{10}}{2*5}=\frac{-30-10\sqrt{10}}{10}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+10\sqrt{10}}{2*5}=\frac{-30+10\sqrt{10}}{10}
$