Final answer:
To solve the quadratic equation 3x²+6x-5=0, we can use the quadratic formula. The solutions to the equation are x = (-6 + 4√6)/(6) and x = (-6 - 4√6)/(6).
Step-by-step explanation:
To solve the quadratic equation 3x²+6x-5=0, we can use the quadratic formula which is derived from the general form of a quadratic equation ax²+bx+c=0. The quadratic formula is:
x = (-b ± √(b²-4ac))/(2a)
Using the coefficients from the given equation, the quadratic formula becomes:
x = (-6 ± √(6²-4(3)(-5)))/(2(3))
Simplifying further, we have:
x = (-6 ± √(36+60))/(6)
x = (-6 ± √(96))/(6)
x = (-6 ± 4√6)/(6)
The solutions to the equation 3x²+6x-5=0 are:
x = (-6 + 4√6)/(6)
x = (-6 - 4√6)/(6)