Solve equation by using the quadratic formula

-3x2-2x-5=0

The quadratic formula is (-b +/- sqrt(b^2 - 4ac))/2a

for an equation in the form ax^2 + bx + c

-3x^2 - 2x - 5 = 0

a = -3
b = -2
c = -5

x = (2 +/- sqrt(4 - 60))/6
x = (2 +/- sqrt(-56))/6
x = (1 +/- i*sqrt(14))/3

To solve the equation -3x^2 - 2x - 5 = 0 using the quadratic formula, we first need to identify the coefficients in the equation:

a = -3
b = -2
c = -5

The quadratic formula is:

x = (-b ± √(b^2 - 4ac)) / (2a)

Plugging in the values of a, b, and c into the quadratic formula, we get:

x = (-(-2) ± √((-2)^2 - 4(-3)(-5))) / (2(-3))

Simplifying further:

x = (2 ± √(4 - 60)) / (-6)
x = (2 ± √(-56)) / (-6)

Since we have a negative value under the square root (√(-56)), we can simplify it by considering it as √(56)i, where i is the imaginary unit.

x = (2 ± √(56)i) / (-6)

Simplifying further:

x = (1 ± √(14)i) / (-3)

Therefore, the two solutions to the equation -3x^2 - 2x - 5 = 0 are:

x = (1 + √(14)i) / (-3)
and
x = (1 - √(14)i) / (-3)