2/5x-18=7/4x+36

Solution for 2/5x-18=7/4x+36 equation:

2/5x-18=7/4x+36

We move all terms to the left:

2/5x-18-(7/4x+36)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 4x+36)!=0

x∈R


We get rid of parentheses

2/5x-7/4x-36-18=0

We calculate fractions


8x/20x^2+(-35x)/20x^2-36-18=0

We add all the numbers together, and all the variables

8x/20x^2+(-35x)/20x^2-54=0

We multiply all the terms by the denominator


8x+(-35x)-54*20x^2=0

Wy multiply elements

-1080x^2+8x+(-35x)=0

We get rid of parentheses

-1080x^2+8x-35x=0

We add all the numbers together, and all the variables

-1080x^2-27x=0

a = -1080; b = -27; c = 0;
Δ = b2-4ac
Δ = -272-4·(-1080)·0
Δ = 729
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{729}=27$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-27)-27}{2*-1080}=\frac{0}{-2160}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-27)+27}{2*-1080}=\frac{54}{-2160}
=-1/40
$