1/10+4x/5x=-9/2x

Solution for 1/10+4x/5x=-9/2x equation:

1/10+4x/5x=-9/2x

We move all terms to the left:

1/10+4x/5x-(-9/2x)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R


We get rid of parentheses

4x/5x+9/2x+1/10=0

We calculate fractions


80x^2/100x^2+20x^2/100x^2+450x/100x^2=0

We multiply all the terms by the denominator


80x^2+20x^2+450x=0

We add all the numbers together, and all the variables

100x^2+450x=0

a = 100; b = 450; c = 0;
Δ = b2-4ac
Δ = 4502-4·100·0
Δ = 202500
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{202500}=450$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(450)-450}{2*100}=\frac{-900}{200}
=-4+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(450)+450}{2*100}=\frac{0}{200}
=0
$