3a^2=18a-21

Solution for 3a^2=18a-21 equation:

3a^2=18a-21

We move all terms to the left:

3a^2-(18a-21)=0

We get rid of parentheses

3a^2-18a+21=0

a = 3; b = -18; c = +21;
Δ = b2-4ac
Δ = -182-4·3·21
Δ = 72
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:

$\sqrt{\Delta}=\sqrt{72}=\sqrt{36*2}=\sqrt{36}*\sqrt{2}=6\sqrt{2}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-6\sqrt{2}}{2*3}=\frac{18-6\sqrt{2}}{6}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+6\sqrt{2}}{2*3}=\frac{18+6\sqrt{2}}{6}
$