Answer:
[tex]\large\boxed{\bold{x = -\frac{4}{3}}}[/tex]
Step-by-step explanation:
[tex]9x^2 + 24x + 20 = 4[/tex]
Bring 4 to the left hand side of the equation.
[tex]9x^{2}+24x+20-4=0 [/tex]
Subtract 4 from 20.
[tex]9x^{2}+24x+16=0 [/tex]
Now, factorise it using the splitting-the-middle-term method .
[tex]9x^{2}+24x+16=0 \\9x^{2}+12x+12x+16 =0\\\left(9x^{2}+12x\right)+\left(12x+16\right)=0 \\3x\left(3x+4\right)+4\left(3x+4\right) =0\\\left(3x+4\right)\left(3x+4\right) = 0\\\left(3x+4\right)^{2} = 0 [/tex]
Now since both the factors are the same, take one of them,
[tex]3x + 4 = 0\\3x = - 4\\\boxed{ \bold{\:x = -\frac{4}{3}}}[/tex]
▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬