3r^2+21r=180

Solution for 3r^2+21r=180 equation:

3r^2+21r=180

We move all terms to the left:

3r^2+21r-(180)=0

a = 3; b = 21; c = -180;
Δ = b2-4ac
Δ = 212-4·3·(-180)
Δ = 2601
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2601}=51$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(21)-51}{2*3}=\frac{-72}{6}
=-12
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+51}{2*3}=\frac{30}{6}
=5
$