6r^2+21r=45

Solution for 6r^2+21r=45 equation:

6r^2+21r=45

We move all terms to the left:

6r^2+21r-(45)=0

a = 6; b = 21; c = -45;
Δ = b2-4ac
Δ = 212-4·6·(-45)
Δ = 1521
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1521}=39$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(21)-39}{2*6}=\frac{-60}{12}
=-5
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+39}{2*6}=\frac{18}{12}
=1+1/2
$