5/7x-1/4x=13

Solution for 5/7x-1/4x=13 equation:

5/7x-1/4x=13

We move all terms to the left:

5/7x-1/4x-(13)=0


Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R



Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We calculate fractions


20x/28x^2+(-7x)/28x^2-13=0

We multiply all the terms by the denominator


20x+(-7x)-13*28x^2=0

Wy multiply elements

-364x^2+20x+(-7x)=0

We get rid of parentheses

-364x^2+20x-7x=0

We add all the numbers together, and all the variables

-364x^2+13x=0

a = -364; b = 13; c = 0;
Δ = b2-4ac
Δ = 132-4·(-364)·0
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(13)-13}{2*-364}=\frac{-26}{-728}
=1/28
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+13}{2*-364}=\frac{0}{-728}
=0
$