Question: does 7x-x+7=3x(x-4+20) have a solution
Simplify the expression.
6x + 7 = 3x^2 -12x + 60x
Since there is an x-squared, the equation is a quadratic. Move all terms to one side and set the equation equal to 0. Combine the like terms.
-3x^2 + 6x + 12x - 60x + 7 = 0
-3x^2 - 42x + 7 = 0
3x^2 + 42x -7 = 0
Use the coefficients for each term to check for the solution(s).
a = 3, b = 42, and c = -7
Since you only want to know if there is a solution, use the discrimanant. It is the expression under the square root in the quadratic formula.
b^2 - 4•a•c
42^2 - 4 • 3 • (-7)