1/4x-2=-6+5/13x

Solution for 1/4x-2=-6+5/13x equation:

1/4x-2=-6+5/13x

We move all terms to the left:

1/4x-2-(-6+5/13x)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 13x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

1/4x-(5/13x-6)-2=0

We get rid of parentheses

1/4x-5/13x+6-2=0

We calculate fractions


13x/52x^2+(-20x)/52x^2+6-2=0

We add all the numbers together, and all the variables

13x/52x^2+(-20x)/52x^2+4=0

We multiply all the terms by the denominator


13x+(-20x)+4*52x^2=0

Wy multiply elements

208x^2+13x+(-20x)=0

We get rid of parentheses

208x^2+13x-20x=0

We add all the numbers together, and all the variables

208x^2-7x=0

a = 208; b = -7; c = 0;
Δ = b2-4ac
Δ = -72-4·208·0
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-7}{2*208}=\frac{0}{416}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+7}{2*208}=\frac{14}{416}
=7/208
$