24=-3(2a-15)a

Solution for 24=-3(2a-15)a equation:

24=-3(2a-15)a

We move all terms to the left:

24-(-3(2a-15)a)=0


We calculate terms in parentheses: -(-3(2a-15)a), so:

-3(2a-15)a

We multiply parentheses

-6a^2+45a

Back to the equation:

-(-6a^2+45a)


We get rid of parentheses

6a^2-45a+24=0

a = 6; b = -45; c = +24;
Δ = b2-4ac
Δ = -452-4·6·24
Δ = 1449
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1449}=\sqrt{9*161}=\sqrt{9}*\sqrt{161}=3\sqrt{161}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-45)-3\sqrt{161}}{2*6}=\frac{45-3\sqrt{161}}{12}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-45)+3\sqrt{161}}{2*6}=\frac{45+3\sqrt{161}}{12}
$