(5x-1=13x-57)X=

Solution for (5x-1=13x-57)X= equation:

(5x-1=13x-57)x=

We move all terms to the left:

(5x-1-(13x-57)x)=0


We calculate terms in parentheses: +(5x-1-(13x-57)x), so:

5x-1-(13x-57)x

determiningTheFunctionDomain
5x-(13x-57)x-1

We multiply parentheses

-13x^2+5x+57x-1

We add all the numbers together, and all the variables

-13x^2+62x-1

Back to the equation:

+(-13x^2+62x-1)


We get rid of parentheses

-13x^2+62x-1=0

a = -13; b = 62; c = -1;
Δ = b2-4ac
Δ = 622-4·(-13)·(-1)
Δ = 3792
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{3792}=\sqrt{16*237}=\sqrt{16}*\sqrt{237}=4\sqrt{237}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(62)-4\sqrt{237}}{2*-13}=\frac{-62-4\sqrt{237}}{-26}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(62)+4\sqrt{237}}{2*-13}=\frac{-62+4\sqrt{237}}{-26}
$