Answer:
[tex]\huge\boxed{\bf\: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{\bf\:x = -\frac{4}{3}}[/tex]
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