Answer: x = (-1 + sqrt(85)) / 6, or x = (-1 - sqrt(85)) / 6
Explanation:
Let's simplify and solve the equation step by step:
Distribute the -5 and -4 on the left side and combine like terms:
-5x + 10 + 4x = 3x^2 - x - 4x + 8 + x + 2
Simplifying the left side and combining like terms on the right side, we get:
-x + 10 = 3x^2 + 3
Subtract 10 from both sides to isolate the variable on one side:
-x = 3x^2 - 7
Add x to both sides to get the quadratic equation in standard form:
3x^2 + x - 7 = 0
Use the quadratic formula to solve for x:
x = (-b ± sqrt(b^2 - 4ac)) / 2a
where a = 3, b = 1, and c = -7. Substituting these values, we get:
x = (-1 ± sqrt(1^2 - 4(3)(-7))) / 2(3)
Simplifying under the square root, we get:
x = (-1 ± sqrt(85)) / 6
Therefore, the solutions to the equation are:
x = (-1 + sqrt(85)) / 6, or x = (-1 - sqrt(85)) / 6
These are approximate values since sqrt(85) is irrational.