Question

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

Answer 1

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