6x^2=-21x-9

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

6x^2=-21x-9

We move all terms to the left:

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

We get rid of parentheses

6x^2+21x+9=0

a = 6; b = 21; c = +9;
Δ = b2-4ac
Δ = 212-4·6·9
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*6}=\frac{-36}{12}
=-3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+15}{2*6}=\frac{-6}{12}
=-1/2
$