-3x^2+10x-3=0
solve the following equations by using the quadratic formula
The quadratic formula is given by:
x = (-b ± √(b^2 - 4ac))/(2a)
For the equation -3x^2 + 10x - 3 = 0, we have:
a = -3, b = 10, and c = -3.
Plugging these values into the quadratic formula, we get:
x = (-10 ± √(10^2 - 4(-3)(-3)))/(2*(-3))
Simplifying further:
x = (-10 ± √(100 - 36))/(-6)
x = (-10 ± √64)/(-6)
x = (-10 ± 8)/(-6)
We can split this solution into two possibilities:
1. x = (-10 + 8)/(-6) = -2/(-6) = 1/3
2. x = (-10 - 8)/(-6) = -18/(-6) = 3
Therefore, the solutions for the equation -3x^2 + 10x - 3 = 0 are x = 1/3 and x = 3.