9=21x+3x^2

Solution for 9=21x+3x^2 equation:

9=21x+3x^2

We move all terms to the left:

9-(21x+3x^2)=0

We get rid of parentheses

-3x^2-21x+9=0

a = -3; b = -21; c = +9;
Δ = b2-4ac
Δ = -212-4·(-3)·9
Δ = 549
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{549}=\sqrt{9*61}=\sqrt{9}*\sqrt{61}=3\sqrt{61}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-21)-3\sqrt{61}}{2*-3}=\frac{21-3\sqrt{61}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+3\sqrt{61}}{2*-3}=\frac{21+3\sqrt{61}}{-6}
$