3a^2=21a+30=0

Solution for 3a^2=21a+30=0 equation:

3a^2=21a+30=0

We move all terms to the left:

3a^2-(21a+30)=0

We get rid of parentheses

3a^2-21a-30=0

a = 3; b = -21; c = -30;
Δ = b2-4ac
Δ = -212-4·3·(-30)
Δ = 801
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:

$\sqrt{\Delta}=\sqrt{801}=\sqrt{9*89}=\sqrt{9}*\sqrt{89}=3\sqrt{89}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-21)-3\sqrt{89}}{2*3}=\frac{21-3\sqrt{89}}{6}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+3\sqrt{89}}{2*3}=\frac{21+3\sqrt{89}}{6}
$