Answer: The required solution set of the given equation is
\(x=\dfrac{5}{2},~~-\dfrac{1}{3}.\)
Step-by-step explanation: We are given to find the solution set of the following quadratic equation:
\(6x^2=13x+5~~~~~~~~~~~~~~~~~~~~~~~~~~(i)\)
We will try to solve the given equation (i) by the method of factorization.
From equation (i), we have
\(6x^2=13x+5\\\\\Rightarrow 6x^2-13x-5=0\\\\\Rightarrow 6x^2-15x+2x-5=0\\\\\Rightarrow 3x(2x-5)+1(2x-5)=0\\\\\Rightarrow (2x-5)(3x+1)=0\\\\\Rightarrow 2x-5=0,~~~~~~~~~3x+1=0\\\\\Rightarrow 2x=5~~~~~~~~~~~\Rightarrow 3x=-1\\\\\\\Rightarrow x=\dfrac{5}{2}~~~~~~~~~~\Rightarrow x=-\dfrac{1}{3}.\)
Thus, the required solution set of the given equation is
\(x=\dfrac{5}{2},~~-\dfrac{1}{3}.\)
