solve equation 10y^3-6y=4y^2

Given the equation:

10y^3 - 6y =4y^2

Solution:

Transpose 4y^2 on the opposite side of the equation, hence we must take note that in transposing a number, the sign changes.

10y^3 - 4y^2 - 6y

Factor out 2y from the equation in order to easily solve for the roots or the solution.

2y (10y^2 -2y - 3)

a = 10

b = -2

c = -3

Now we need to solve for the value of y. To do so, we will use the quadratic formula. 

The Quadratic formula:

x = −b ± √(b^2 − 4ac)/2a

is used to solve quadratic equations where a ≠ 0, in the form
ax^2+bx+c=0

When b^2−4ac=0 there is one real root.

When b^2−4ac>0 there are two real roots.

When b^2−4ac<0 there are no real roots, only a complex number.

Substitute the given values of a, b and c to the quadratic formula.

x = −b ± √(b^2 − 4ac)/2a

x = −(-2) ± √(-2^2 − 4(10)(-3))/2(10)

x = 2 ± √(4 + 120)/20

x = 2 ± √(124)/20

x = 2 ± 11.14/20

Solve for + - separately.

x = 2 + 11.14/20

x = 13.14/20

x= 0.66

x = 2 - 11.14/20

x = -9.14/20

x = -0.46

Final answer:

x= 0.66

x = -0.46