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
