2/5x-5=3/4x-4

Solution for 2/5x-5=3/4x-4 equation:

2/5x-5=3/4x-4

We move all terms to the left:

2/5x-5-(3/4x-4)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 4x-4)!=0

x∈R


We get rid of parentheses

2/5x-3/4x+4-5=0

We calculate fractions


8x/20x^2+(-15x)/20x^2+4-5=0

We add all the numbers together, and all the variables

8x/20x^2+(-15x)/20x^2-1=0

We multiply all the terms by the denominator


8x+(-15x)-1*20x^2=0

Wy multiply elements

-20x^2+8x+(-15x)=0

We get rid of parentheses

-20x^2+8x-15x=0

We add all the numbers together, and all the variables

-20x^2-7x=0

a = -20; b = -7; c = 0;
Δ = b2-4ac
Δ = -72-4·(-20)·0
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-7}{2*-20}=\frac{0}{-40}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+7}{2*-20}=\frac{14}{-40}
=-7/20
$