5r(2r+6)=180

Solution for 5r(2r+6)=180 equation:

5r(2r+6)=180

We move all terms to the left:

5r(2r+6)-(180)=0

We multiply parentheses

10r^2+30r-180=0

a = 10; b = 30; c = -180;
Δ = b2-4ac
Δ = 302-4·10·(-180)
Δ = 8100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{8100}=90$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-90}{2*10}=\frac{-120}{20}
=-6
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+90}{2*10}=\frac{60}{20}
=3
$