3x(3x+8)=-7

Solution for 3x(3x+8)=-7 equation:

3x(3x+8)=-7

We move all terms to the left:

3x(3x+8)-(-7)=0

We add all the numbers together, and all the variables

3x(3x+8)+7=0

We multiply parentheses

9x^2+24x+7=0

a = 9; b = 24; c = +7;
Δ = b2-4ac
Δ = 242-4·9·7
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-18}{2*9}=\frac{-42}{18}
=-2+1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+18}{2*9}=\frac{-6}{18}
=-1/3
$