Final answer:
To solve the equation 2w^2 - 15w + 19 = 0, we can use the quadratic formula. The solutions are w = (15 + sqrt(73)) / 4 and w = (15 - sqrt(73)) / 4.
Step-by-step explanation:
To solve the equation 2w^2 - 15w + 19 = 0, we can use the quadratic formula. The quadratic formula states that for an equation of the form ax^2 + bx + c = 0, the solutions are given by:
x = (-b ± sqrt(b^2 - 4ac)) / (2a)
Applying this formula to our equation, we have:
w = (-(-15) ± sqrt((-15)^2 - 4(2)(19))) / (2(2))
w = (15 ± sqrt(225 - 152)) / 4
w = (15 ± sqrt(73)) / 4
Therefore, the solutions for the equation are w = (15 + sqrt(73)) / 4 and w = (15 - sqrt(73)) / 4.