Final answer:
This quadratic equation using the quadratic formula to find the possible values of x as -10 and 4.
Step-by-step explanation:
To solve the equation x^2:(20-3x)=1:2, we can start by cross multiplying:
x^2 = 2(20 - 3x)
Expanding and simplifying:
x^2 = 40 - 6x
Bringing all terms to one side:
x^2 + 6x - 40 = 0
Now we can solve this quadratic equation by factoring, completing the square, or using the quadratic formula. Let's use the quadratic formula:
x = (-6 ± √(6^2 - 4(1)(-40)))/(2(1))
Simplifying further:
x = (-6 ± √(36 + 160))/2
x = (-6 ± √196)/2
x = (-6 ± 14)/2
So the possible values of x are -10 and 4.