9x^2=-3-12x

Solution for 9x^2=-3-12x equation:

9x^2=-3-12x

We move all terms to the left:

9x^2-(-3-12x)=0

We add all the numbers together, and all the variables

9x^2-(-12x-3)=0

We get rid of parentheses

9x^2+12x+3=0

a = 9; b = 12; c = +3;
Δ = b2-4ac
Δ = 122-4·9·3
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-6}{2*9}=\frac{-18}{18}
=-1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+6}{2*9}=\frac{-6}{18}
=-1/3
$