26n 2 +41n+20=6n 2

The equation you've given is: 26n^2 + 41n + 20 = 6n^2

First, let's simplify the equation by subtracting 6n^2 from both sides:

26n^2 - 6n^2 + 41n + 20 = 0

This simplifies to:

20n^2 + 41n + 20 = 0

This is a quadratic equation in the form of ax^2 + bx + c = 0. We can solve it using the quadratic formula, which is:

n = [-b ± sqrt(b^2 - 4ac)] / (2a)

Here, a = 20, b = 41, and c = 20. Substituting these values into the quadratic formula gives:

n = [-41 ± sqrt((41)^2 - 42020)] / (2*20)

Calculating the values under the square root:

n = [-41 ± sqrt(1681 - 1600)] / 40

n = [-41 ± sqrt(81)] / 40

Taking the square root of 81 gives 9, so:

n = [-41 ± 9] / 40

This gives us two solutions:

n1 = (-41 + 9) / 40 = -32 / 40 = -0.8

n2 = (-41 - 9) / 40 = -50 / 40 = -1.25

So, the solutions to the equation 26n^2 + 41n + 20 = 6n^2 are n = -0.8 and n = -1.25.