Analyze the equation you are going to solve adequately. Look carefully at the coefficients of the unknown value and the constant, c. For instance in the equation 2x^2 +10x+12=0, the coefficients of the unknown are 2 and 10 while the constant is 12.
Simplify the coefficients by dividing them by a smaller number. In this case, since all the coefficients are divisible by 2, divide all the numbers by two including the zero. The result will produce a quadratic equation of the form x^2+5x+6=0.
Look for a pair of numbers that would give the coefficient of x when added together and the product of the coefficient of x^2 and the constant when multiplied. On this example, the number pair is 2 and 3.
Write the initial equation with the number pair you have just obtained. This equation will take the form x^2+2x+3x+6=0. Factorize the new equation into two distinct roots. In this case, the two roots are (x+2)(x+3)=0.
Equate both roots to zero, that is x+2=0 and x+3=0. Collecting likes terms together, the solutions for x are -2 and -3.
Analyze the equation at hand, again checking the coefficients and the constant. For this procedure, use the previous example.
Fix the coefficients of the unknown and the constant in the appropriate positions in the general quadratic formula equation. The general quadratic formula is x=((-b)+SQRT((b*b)-4*a*c))/(2*a) and x=((-b)-SQRT((b*b)-4*a*c))/(2*a).The equation appears to have two formulas because each quadratic equation has two roots.
Use a calculator to perform the calculation. Input values of a, b and c into the equations to get the answers. In this case, using the first equation, x= ((-5)+SQRT((5*5)-4*1*6))/(2*1) and you get an answer of -2. Using the second equation, x= ((-5)-SQRT ((5*5)-4*1*6))/(2*1) and you get an answer of -3. Therefore, the equation has two distinct roots: -2 and -3.