SOLUTION: Solve using quadratic formula. 5x^2-x+3=0

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Let's use the quadratic formula to solve for x:


Starting with the general quadratic



the general solution using the quadratic equation is:



So lets solve ( notice , , and )

Plug in a=5, b=-1, and c=3



Negate -1 to get 1



Square -1 to get 1 (note: remember when you square -1, you must square the negative as well. This is because .)



Multiply to get



Combine like terms in the radicand (everything under the square root)



Simplify the square root (note: If you need help with simplifying the square root, check out this solver)



Multiply 2 and 5 to get 10



After simplifying, the quadratic has roots of

or

Notice if we graph the quadratic , we get

graph of

And we can see that there are no real roots

To visually verify the answer, check out this page to see a visual representation of imaginary roots

You can put this solution on YOUR website!
5x^2-x+3=0

x=(1+-sqrt[-1^2-4*5*3])/2*5
x=(1+-sqrt[1-60])/10
x=(1+-sqrt-59)/10
x=(1+-7.68i)/10
x=1/10+7.68i/10
x=.1+.768i answer.
x=(1-7.68i)/10
x=.1-.768i answer.