-4/5x+5/4=1/4x+4

Solution for -4/5x+5/4=1/4x+4 equation:

-4/5x+5/4=1/4x+4

We move all terms to the left:

-4/5x+5/4-(1/4x+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

-4/5x-1/4x-4+5/4=0

We calculate fractions


(-256x)/320x^2+(-5x)/320x^2+25x/320x^2-4=0

We multiply all the terms by the denominator


(-256x)+(-5x)+25x-4*320x^2=0

We add all the numbers together, and all the variables

25x+(-256x)+(-5x)-4*320x^2=0

Wy multiply elements

-1280x^2+25x+(-256x)+(-5x)=0

We get rid of parentheses

-1280x^2+25x-256x-5x=0

We add all the numbers together, and all the variables

-1280x^2-236x=0

a = -1280; b = -236; c = 0;
Δ = b2-4ac
Δ = -2362-4·(-1280)·0
Δ = 55696
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{55696}=236$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-236)-236}{2*-1280}=\frac{0}{-2560}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-236)+236}{2*-1280}=\frac{472}{-2560}
=-59/320
$