5/2x+8/5x=-41/10

Solution for 5/2x+8/5x=-41/10 equation:

5/2x+8/5x=-41/10

We move all terms to the left:

5/2x+8/5x-(-41/10)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We get rid of parentheses

5/2x+8/5x+41/10=0

We calculate fractions


2050x^2/100x^2+250x/100x^2+160x/100x^2=0

We multiply all the terms by the denominator


2050x^2+250x+160x=0

We add all the numbers together, and all the variables

2050x^2+410x=0

a = 2050; b = 410; c = 0;
Δ = b2-4ac
Δ = 4102-4·2050·0
Δ = 168100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{168100}=410$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(410)-410}{2*2050}=\frac{-820}{4100}
=-1/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(410)+410}{2*2050}=\frac{0}{4100}
=0
$