Solution:
[tex]3 {x}^{2} = - 4 + 8x[/tex]
Let us transpose -4 and 8x to the Left Hand Side. So we are left with 0 on the Right Hand Side.
[tex] = > {3x}^{2} + 4 - 8x = 0[/tex]
Now, arrange the expression in standard form.
[tex] = > {3x}^{2} - 8x + 4 = 0 \\ [/tex]
Now, split the mid term. Here, 3 × 4 = 12. So, we can split -8x into -2x and -6x.
[tex] = > ({3x}^{2} - 6x )- (2x + 4) = 0 \\ [/tex]
Now, take 3x common from the first expression and 2 from the second.
[tex] = > 3x(x - 2) - 2(x - 2) = 0 \\ = > (3x - 2)(x - 2) = 0[/tex]
When, two terms are equal to 0, then each term is equal to zero.
[tex] = > 3x - 2 = 0 \: \: and \: x - 2 = 0 \\ = > 3x = 2 \: \: and \: x = 2 \\ = > x = \frac{2}{3} \: \: and \: \: 2[/tex]
Answer:
[tex]x = \frac{2}{3} \: \: and \: \: 2[/tex]
Hope you could understand.
If you have any query, feel free to ask.
