Answer:
3x2 – 10x + 6 = 0
Explanation:
Givena general quadratic equation
ax²+bx+c = 0
The general formula for finding x is;
x = -b±√b²-4ac/2a
Where a,b and c are the coefficient of x², x and x° respectively
Given the solution in question to be;
x = 5±2√7/3
The quadratic equation that has thw above general solution will be;
3x²-10x+6 = 0
From the equation, a = 3, b= -10 and c = 6
Substituting this value in the general formula to get x we have;
x = -(-10)±√(-10)²-4(3)(6)/2(3)
x = 10±√100-72/6
x = 10±√28/6
x = 10±√7×4/6
x = 10±2√7/6
Dividing through by 2 gave;
x = 2(5±2√7)/6
x = 5±2√7/3 (which gives the solution in question)