9x^2=-21x-6

Solution for 9x^2=-21x-6 equation:

9x^2=-21x-6

We move all terms to the left:

9x^2-(-21x-6)=0

We get rid of parentheses

9x^2+21x+6=0

a = 9; b = 21; c = +6;
Δ = b2-4ac
Δ = 212-4·9·6
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(21)-15}{2*9}=\frac{-36}{18}
=-2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+15}{2*9}=\frac{-6}{18}
=-1/3
$