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

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

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

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 5x+13)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


25x/10x^2+(-8x)/10x^2-13-4=0

We add all the numbers together, and all the variables

25x/10x^2+(-8x)/10x^2-17=0

We multiply all the terms by the denominator


25x+(-8x)-17*10x^2=0

Wy multiply elements

-170x^2+25x+(-8x)=0

We get rid of parentheses

-170x^2+25x-8x=0

We add all the numbers together, and all the variables

-170x^2+17x=0

a = -170; b = 17; c = 0;
Δ = b2-4ac
Δ = 172-4·(-170)·0
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(17)-17}{2*-170}=\frac{-34}{-340}
=1/10
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+17}{2*-170}=\frac{0}{-340}
=0
$