Question

find the roots of 3(x-4)²-5(x-4)=12

Answer 1

Heyyy....
Solution is done.

see in this picture.

HOPE it helps U. :-)

Answer 2

First expand them,

3(x²+16-8x) -5(x-4) = 12
=> 3x² + 48 - 24x -5x + 20 = 12,
=> 3x² - 29x + 56 = 0,

Now use the quadratic equation formula, or find the factors,

In general x of quadratic equation is,
$\frac{( -b + - \sqrt{ {b}^{2} - 4ac} )}{2a}$

Here a = 3, b = -29 , c = 56,

Inserting them in the formula we get,
(29+- √169 )/6 ,. b²-4ac = 169,

=> (29+-13)/6,
=> 42/6 and 16/6, are the roots,
=> 7 and 16/6,
=> 7, 8/3 are the roots

Keep them in the question, you will get 12,

There is another simpler method to do this problem,

3x² - 29x +56 = 0, can be written as,
3x² - 21x - 8x + 56 = 0,
Now taking common,
3x(x-7) -8(x-7) = 0,

Taking ( x-7 ) common,
(x-7)[3x-8] = 0
=> Either x -7 = 0 or 3x - 8 =0,
=> either x = 7 or x = 8/3, But as it is a quadratic , both are the roots of the equation,

Hope you understand,

Have a great day !!