Solve the equation 3x^2 +17x -6 = 0 without using a calculator

In order to solve this equation without using a calculator we will need to factorise. The first step in factorising this equation is to rewrite our 17x as two separate terms. The coefficients of these need to multiply to make -18 (the product of the coefficient of x² and our constant, which is 3 x -6). The coefficients also need to add to make 17 (the coefficient of x). The numbers 18 and -1 fit this criteria so we can now rewrite our equation using 18x and -x to replace 17x.This gives us 3x² + 18x -x -6=0. To factorise we then look at the first two terms and the second two terms of the equation separately and take the greatest common factor of each of these.This gives 3x(x+6) - (x+6)=0. As (x+6) appears twice we can further simplify this equation to (3x-1)(x+6)=0, taking the common factor (x+6) and the two terms outside of the brackets (3x-1).Therefore 3x-1=0 and x+6=0, so x=1/3 and x=-6.