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

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

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

We move all terms to the left:

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


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We get rid of parentheses

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

We calculate fractions


20x^2/100x^2+80x/100x^2+50x/100x^2=0

We multiply all the terms by the denominator


20x^2+80x+50x=0

We add all the numbers together, and all the variables

20x^2+130x=0

a = 20; b = 130; c = 0;
Δ = b2-4ac
Δ = 1302-4·20·0
Δ = 16900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16900}=130$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(130)-130}{2*20}=\frac{-260}{40}
=-6+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(130)+130}{2*20}=\frac{0}{40}
=0
$