−3w 2 +8w+10=−4w 2

Sure, let's solve the equation step by step:

Given equation is: −3w^2 + 8w + 10 = −4w^2

Step 1: Move all terms to one side of the equation to set the equation to zero.

This gives us: −3w^2 + 4w^2 + 8w + 10 = 0

Step 2: Simplify the equation.

This gives us: w^2 + 8w + 10 = 0

This is a quadratic equation in the form of ax^2 + bx + c = 0.

To solve for w, we can use the quadratic formula, which is w = [-b ± sqrt(b^2 - 4ac)] / 2a

Here, a = 1, b = 8, and c = 10.

Step 3: Substitute a, b, and c into the quadratic formula and solve for w.

This gives us: w = [-8 ± sqrt((8)^2 - 4110)] / 2*1 = [-8 ± sqrt(64 - 40)] / 2 = [-8 ± sqrt(24)] / 2 = [-8 ± 2sqrt(6)] / 2 = -4 ± sqrt(6)

So, the solutions for w are w = -4 + sqrt(6) and w = -4 - sqrt(6).