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

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

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

We move all terms to the left:

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

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

We calculate fractions


5x/20x^2+16x/20x^2+4=0

We multiply all the terms by the denominator


5x+16x+4*20x^2=0

We add all the numbers together, and all the variables

21x+4*20x^2=0

Wy multiply elements

80x^2+21x=0

a = 80; b = 21; c = 0;
Δ = b2-4ac
Δ = 212-4·80·0
Δ = 441
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{441}=21$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(21)-21}{2*80}=\frac{-42}{160}
=-21/80
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+21}{2*80}=\frac{0}{160}
=0
$