5-2/7x=1/2x+13

Solution for 5-2/7x=1/2x+13 equation:

5-2/7x=1/2x+13

We move all terms to the left:

5-2/7x-(1/2x+13)=0


Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R



Domain of the equation: 2x+13)!=0

x∈R


We get rid of parentheses

-2/7x-1/2x-13+5=0

We calculate fractions


(-4x)/14x^2+(-7x)/14x^2-13+5=0

We add all the numbers together, and all the variables

(-4x)/14x^2+(-7x)/14x^2-8=0

We multiply all the terms by the denominator


(-4x)+(-7x)-8*14x^2=0

Wy multiply elements

-112x^2+(-4x)+(-7x)=0

We get rid of parentheses

-112x^2-4x-7x=0

We add all the numbers together, and all the variables

-112x^2-11x=0

a = -112; b = -11; c = 0;
Δ = b2-4ac
Δ = -112-4·(-112)·0
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-11}{2*-112}=\frac{0}{-224}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+11}{2*-112}=\frac{22}{-224}
=-11/112
$