2y 2 −19y+17=−3y 2

The given equation is: 2y^2 - 19y + 17 = -3y^2

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

2y^2 + 3y^2 + 19y - 17 = 0

Step 2: Simplify the equation:

5y^2 + 19y - 17 = 0

Step 3: This is a quadratic equation in the form of ax^2 + bx + c = 0. We can solve it using the quadratic formula, which is y = [-b ± sqrt(b^2 - 4ac)] / 2a.

Here, a = 5, b = 19, and c = -17.

Step 4: Substitute a, b, and c into the quadratic formula:

y = [-19 ± sqrt((19)^2 - 45(-17))] / 2*5 y = [-19 ± sqrt(361 + 340)] / 10 y = [-19 ± sqrt(701)] / 10

So, the solutions of the equation are y = [-19 + sqrt(701)] / 10 and y = [-19 - sqrt(701)] / 10.