5/4x-2/5x-13=24

Solution for 5/4x-2/5x-13=24 equation:

5/4x-2/5x-13=24

We move all terms to the left:

5/4x-2/5x-13-(24)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We add all the numbers together, and all the variables

5/4x-2/5x-37=0

We calculate fractions


25x/20x^2+(-8x)/20x^2-37=0

We multiply all the terms by the denominator


25x+(-8x)-37*20x^2=0

Wy multiply elements

-740x^2+25x+(-8x)=0

We get rid of parentheses

-740x^2+25x-8x=0

We add all the numbers together, and all the variables

-740x^2+17x=0

a = -740; b = 17; c = 0;
Δ = b2-4ac
Δ = 172-4·(-740)·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*-740}=\frac{-34}{-1480}
=17/740
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+17}{2*-740}=\frac{0}{-1480}
=0
$