3a^2=27a-24

Solution for 3a^2=27a-24 equation:

3a^2=27a-24

We move all terms to the left:

3a^2-(27a-24)=0

We get rid of parentheses

3a^2-27a+24=0

a = 3; b = -27; c = +24;
Δ = b2-4ac
Δ = -272-4·3·24
Δ = 441
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{441}=21$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-27)-21}{2*3}=\frac{6}{6}
=1
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-27)+21}{2*3}=\frac{48}{6}
=8
$