2x2 + 4x − 5 = 0

To solve the quadratic equation 2x^2 + 4x - 5 = 0, we can use the quadratic formula:

x = (-b ± sqrt(b^2 - 4ac)) / 2a

In this equation, the coefficients are:
a = 2
b = 4
c = -5

Plug these values into the quadratic formula:

x = (-4 ± sqrt(4^2 - 4(2)(-5))) / 2(2)

x = (-4 ± sqrt(16 + 40)) / 4

x = (-4 ± sqrt(56)) / 4

Now, we can find the two possible solutions for x:

x_1 = (-4 + sqrt(56)) / 4

x_2 = (-4 - sqrt(56)) / 4

These are the roots of the quadratic equation 2x^2 + 4x - 5 = 0.