Answer: The correct option is (b) [tex]4x^2-14x+15=0.[/tex]
Step-by-step explanation: The given equation is
[tex]13-6x=(2x-5)^2+3.~~~~~~~~~~~~~(i)[/tex]
We are given to select the correct standard form of the above equation.
We will be using the following formula:
[tex](a-b)^2=a^2-2ab+b^2.[/tex]
From equation (i), we have
[tex]13-6x=(2x-5)^2+3\\\\\Rightarrow 13-6x=4x^2-20x+25+3\\\\\Rightarrow 13-6x=4x^2-20x+28\\\\\Rightarrow 4x^2-20x+28-13+6x=0\\\\\Rightarrow 4x^2-14x+15=0.[/tex]
Therefore, the correct standard form is [tex]4x^2-14x+15=0.[/tex]
Thus, (b) is the correct option.
