Answer:
(3 +/- i*sqrt(151) / 20 (no real solutions)
Explanation:
10x^2 - 6x + 4 = -3x
Add 3x to both sides
10x^2 - 6x + 4 + 3x = -3x + 3x
10x^2 - 6x + 4 + 3x = 0
Add like terms
10x^2 - 3x + 4 = 0
We have to use quadratic formula to find the answers
For this equation, a = 10, b = -3 and c = 4
Note: +/- is plus or minus
Quadratic formula:
x = (-b +/- sqrt(b^2 - 4ac)) / 2a
x = (-(-3) +/- sqrt(-3^2 - 4(10)(4))) / 2(10)
x = (3 +/- sqrt(9 - 160)) / 20
x = (3 +/- sqrt(-151) / 20
x = (3 +/- i*sqrt(151) / 20
if there's a "-" sign inside a square root, it will give you an imaginary number.
Example:
-sqrt(9) = -3
sqrt(-9) = 3i (first you will ignore the "- " sign, then square the number. After finding the square root, take that '-' sign and turn it to an "i")
So for sqrt(-151), 151 is not a perfect square, so you will get a decimal number. Leave it as it is:
sqrt(151). We can't forget about the "-". Turn the minus into a sign.
It will be i*sqrt(151)
Imaginary numbers can't be simplified, so this is the answer.
(3 +/- i*sqrt(151) / 20