13/4x+7=5/2x+13

Solution for 13/4x+7=5/2x+13 equation:

13/4x+7=5/2x+13

We move all terms to the left:

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


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



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

x∈R


We get rid of parentheses

13/4x-5/2x-13+7=0

We calculate fractions


26x/8x^2+(-20x)/8x^2-13+7=0

We add all the numbers together, and all the variables

26x/8x^2+(-20x)/8x^2-6=0

We multiply all the terms by the denominator


26x+(-20x)-6*8x^2=0

Wy multiply elements

-48x^2+26x+(-20x)=0

We get rid of parentheses

-48x^2+26x-20x=0

We add all the numbers together, and all the variables

-48x^2+6x=0

a = -48; b = 6; c = 0;
Δ = b2-4ac
Δ = 62-4·(-48)·0
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-6}{2*-48}=\frac{-12}{-96}
=1/8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+6}{2*-48}=\frac{0}{-96}
=0
$