4x^ (2) = 13x-3 use quadratic formula

The quadratic formula is - b + / - sqrt (b^2-4ac) all over 2a.

First we have to get all the variables on one side so ... Subtract 4x: 0=-4x^ (2) + 13x-3

OR add 3 and subtract 13x: 4x^ (2) - 13x+3=0

Since I prefer a to be positive, I'm going to choose the second equation.

So ... now we just plug and chug. a is the value of the variable squared. In this case a=4. b is the value with the variable, or b=-13. c is the last term. c=3

**Remember: Ax^ (2) + By+C**

Now we just plug everything in.

-b = 13 (negative minus a negative is a positive)

+/-sqrt ((-13) ^ (2) - 4 (4) (3))

all over 2 (4)

So work with the radical first.

(-13) ^2=169

4 (4) (3) = 48

+/-sqrt (169-48)

+-sqrt (121)

sqrt (121) = 11

Now it's just: (13+/-11) / 2 (4)

(13+/-11) / 8

Split this into two equations:

(13+11) / 8

(13-11) / 8

Solve both: 24/8=3

2/8=1/4

So x = 3, 1/4

Plug them back in and see if there's one solution or two:

4 (3) ^2=13 (3) - 3

36=36

So x=3.

How about 1/4?:

4 (1/4) ^2=13 (1/4) - 3

4 (1/16) = 13/4-3

4/16=13/4-3

1/4=13/4-3

1/4=13/4 - (3x4) / (1x4) * Like denominators to add or subtract*

1/4=13/4-12/4

1/4=1/4.

So x=1/4.

In this case, both answers work. So the answer, using the quadratic formula is x=1/4, x=3