# `4x^2 -24x + 1 = 0`

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To solve this equation and any quadratic equation `ax^2+bx+c=0` you can use the following formula

`x_(1,2)=(-bpm sqrt(b^2-4ac))/(2a)`

In your case `a=4,` `b=-24` and `c=1.`

`x_(1,2)=(24pm sqrt((-24)^2-4cdot4cdot1))/(2cdot4)=`

`(24pm sqrt(576-16))/8=(24pm4sqrt(35))/8=(6pm sqrt(35))/2`

`x_1=(6-sqrt(35))/2approx0.0419601`

`x_2=(6+sqrt(35))/2approx5.95804`

`4x^2-24x+1=0`

`4x^2-24x+36+1=36```

`(2x-6)^2=35`

`2x-6=+-sqrt(35)`

`2x=6+-sqrt(35)`

`x=(6+-sqrt(35))/2`

`x_1=5.958039891`

`x_2=0.041960108`