15x 22x - 6) = 10x + 7

What is x?

x = 1/66 + sqrt (863/5) / 66 or x = 1/66 - sqrt (863/5) / 66

Step-by-step explanation:

Solve for x:

330 x^2 - 6 = 10 x + 7

Subtract 10 x + 7 from both sides:

330 x^2 - 10 x - 13 = 0

Divide both sides by 330:

x^2 - x/33 - 13/330 = 0

Add 13/330 to both sides:

x^2 - x/33 = 13/330

Add 1/4356 to both sides:

x^2 - x/33 + 1/4356 = 863/21780

Write the left hand side as a square:

(x - 1/66) ^2 = 863/21780

Take the square root of both sides:

x - 1/66 = sqrt (863/5) / 66 or x - 1/66 = - sqrt (863/5) / 66

Add 1/66 to both sides:

x = 1/66 + sqrt (863/5) / 66 or x - 1/66 = - sqrt (863/5) / 66

Add 1/66 to both sides:

Answer: x = 1/66 + sqrt (863/5) / 66 or x = 1/66 - sqrt (863/5) / 66