9x2+27x=-14

Solution for 9x2+27x=-14 equation:

9x^2+27x=-14

We move all terms to the left:

9x^2+27x-(-14)=0

We add all the numbers together, and all the variables

9x^2+27x+14=0

a = 9; b = 27; c = +14;
Δ = b2-4ac
Δ = 272-4·9·14
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{-(27)-15}{2*9}=\frac{-42}{18}
=-2+1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(27)+15}{2*9}=\frac{-12}{18}
=-2/3
$