Question

What is the solution set of the following equation?
6x^2 = 13x + 5

Answer 1

Answer: The required solution set of the given equation is

`x=(5)/(2),~~-(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=(5)/(2)~~~~~~~~~~\Rightarrow x=-(1)/(3).`

Thus, the required solution set of the given equation is

`x=(5)/(2),~~-(1)/(3).`

Answer 2

6x^2 = 13x + 5
6x^2 - 13x - 5 = 0
6x^2 + 2x - 15x - 5 = 0
2x(3x + 1) - 5(3x + 1) = 0
(2x - 5)(3x + 1) = 0
2x - 5 = 0 or 3x + 1 = 0
2x = 5 or 3x = -1
x = 5/2 or x = -1/3
solution set is 5/2, -1/3.