x-1/4x-5=13

Solution for x-1/4x-5=13 equation:

x-1/4x-5=13

We move all terms to the left:

x-1/4x-5-(13)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We add all the numbers together, and all the variables

x-1/4x-18=0

We multiply all the terms by the denominator


x*4x-18*4x-1=0

Wy multiply elements

4x^2-72x-1=0

a = 4; b = -72; c = -1;
Δ = b2-4ac
Δ = -722-4·4·(-1)
Δ = 5200
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:

$\sqrt{\Delta}=\sqrt{5200}=\sqrt{400*13}=\sqrt{400}*\sqrt{13}=20\sqrt{13}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-72)-20\sqrt{13}}{2*4}=\frac{72-20\sqrt{13}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-72)+20\sqrt{13}}{2*4}=\frac{72+20\sqrt{13}}{8}
$