You may use quadratic formula such that:

`x_(1,2) = (-b +- sqrt(b^2 - 4ac))/(2a)`

You need find the coefficients a,b,c such that:

`a = 1 , b = -7, c = 12`

You need to substitute the coefficients in equation, such that:

`x_(1,2) = (-(-7) +- sqrt((-7)^2 - 4*1*12))/(2*1)`

`x_(1,2) = (7 +- sqrt(49 - 48))/2`

`x_(1,2) = (7 +-1)/2 => {(x_1 = (7+1)/2),(x_2 = (7-1)/2):}`

`{(x_1 = 4),(x_2 = 3):}`

Hence, evaluating the solutions to quadratic equation, using quadratic formula, yields `x_1 = 4` and `x_2 = 3.`

The equation x^2-7x+12=0 has to be solved.

Factor the expression on the left and equate each term of the product to 0 to determine the appropriate value of x.

x^2-7x+12=0

x^2 - 4x - 3x + 12 = 0

x(x - 4) - 3(x - 4) = 0

(x - 3)(x - 4) = 0

x - 3 = 0 gives x = 3 and x - 4 = 0 gives x = 4

The solution of the equation x^2-7x+12=0 is x = 3 and x - 4

We'll identify the sum and product of the roots of the quadratic in the given equation:

x^2 - 7x + 12 = 0

S = 7 and P = 12

We'll apply Viete's relations:

x1+x2=7

x1*x2=12

x1 = 3 and x2 = 4

The solutions of the given quadratic are: x1 = 3 and x2 = 4