A little attempt to write Maths in English (I know it is not a common topic when you learn a language, but I'm studying Physics, so it's important for me to know how to write Maths propperly in English. I would like to know if the text sounds natural as if it would be real) ///////////////// In the next short article we will try to show how to get the expression for the roots of a second-order linear equation using squares of first-order polynomials whose roots will be the roots of the second-order linear equation: a*x^2 + b*x + c = 0 (I) To avoid any kind of misunderstanding is needed to explain what some expressions mean: - 'alpha*beta' symbol means alpha times beta - 'alpha/beta' means alpha divided by beta - 'alpha^(beta)' means raise the number or expression alpha to the power of beta, which could be a number or an algebraic expression - 'sqrt(alpha)' means the square root of alpha. Let be 'x_1' and 'x_2' the two roots of the equation (I) whose variable is 'x'. We are trying to write the previous equation as perfect square of two first-order polynomials with roots 'x_1' and 'x_2': (x-x_1)*(x-x_2) = 0 (II) Now, we will multiply both sides of (I) by '4*a': 4*(a^2)*(x^2) + 4*a*b*x + 4*a*c = 0 (III) Adding to both sides of (IV) 'b^2' we got: 4*(a^2)*(x^2) + 4*a*b*x + 4*a*c + b^2 = b^2 (IV) Moving '4*a*c' to the right side we have: 4*(a^2)*(x^2) + 4*a*b*x + b^2 = b^2 - 4*a*c (V) Now, if we remember that a perfect square is: (alpha + beta)^2 = alpha^2 + 2*alpha*beta + beta^2 (VI) we see that the left side of (VI) is already a perfect square, so we can write (VI) as follows: (2*a*x + b)^2 = b^2 - 4*a*c (VII) Taking the square root to both sides of (VIII) we have two options: 2*a*x_1 + b = sqrt(b^2 - 4*a*c) => x_1 = (-b + sqrt(b^2 - 4*a*c))/(2*a) (VIII) 2*a*x_1 + b = - sqrt(b^2 - 4*a*c) => x_2 = (-b - sqrt(b^2 - 4*a*c))/(2*a) (IX) And the problem is resolved, because we have already obtained the expression we were looking for.