6r(5+2r)=24

Solution for 6r(5+2r)=24 equation:

6r(5+2r)=24

We move all terms to the left:

6r(5+2r)-(24)=0

We add all the numbers together, and all the variables

6r(2r+5)-24=0

We multiply parentheses

12r^2+30r-24=0

a = 12; b = 30; c = -24;
Δ = b2-4ac
Δ = 302-4·12·(-24)
Δ = 2052
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:

$\sqrt{\Delta}=\sqrt{2052}=\sqrt{36*57}=\sqrt{36}*\sqrt{57}=6\sqrt{57}$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-6\sqrt{57}}{2*12}=\frac{-30-6\sqrt{57}}{24}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+6\sqrt{57}}{2*12}=\frac{-30+6\sqrt{57}}{24}
$