Final answer:
To solve the equation 6w^2 + 19w - 15 = -4w^2, we can use the quadratic formula. The solutions are w = 0.6 and w = -2.5.
Step-by-step explanation:
To solve the equation 6w^2 + 19w - 15 = -4w^2, we can start by combining like terms to get:
10w^2 + 19w - 15 = 0
Next, we can rearrange the equation to get it in the form ax^2 + bx + c = 0:
10w^2 + 19w - 15 = 0
Now, we can use the quadratic formula to find the solutions:
w = (-b ± sqrt(b^2 - 4ac)) / (2a)
Substituting the values of a = 10, b = 19, and c = -15 into the formula, we get:
w = (-19 ± sqrt(19^2 - 4*10*(-15))) / (2*10)
w = (-19 ± sqrt(361 + 600)) / 20
w = (-19 ± sqrt(961)) / 20
w = (-19 ± 31) / 20
So the two real solutions for w are:
w = (-19 + 31) / 20 = 12/20 = 0.6
w = (-19 - 31) / 20 = -50/20 = -2.5