5x(3x+2)=-9x-6

Solution for 5x(3x+2)=-9x-6 equation:

5x(3x+2)=-9x-6

We move all terms to the left:

5x(3x+2)-(-9x-6)=0

We multiply parentheses

15x^2+10x-(-9x-6)=0

We get rid of parentheses

15x^2+10x+9x+6=0

We add all the numbers together, and all the variables

15x^2+19x+6=0

a = 15; b = 19; c = +6;
Δ = b2-4ac
Δ = 192-4·15·6
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(19)-1}{2*15}=\frac{-20}{30}
=-2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(19)+1}{2*15}=\frac{-18}{30}
=-3/5
$