2/5a+2=-3/10a-5

Solution for 2/5a+2=-3/10a-5 equation:

2/5a+2=-3/10a-5

We move all terms to the left:

2/5a+2-(-3/10a-5)=0


Domain of the equation: 5a!=0

a!=0/5

a!=0

a∈R



Domain of the equation: 10a-5)!=0

a∈R


We get rid of parentheses

2/5a+3/10a+5+2=0

We calculate fractions


20a/50a^2+15a/50a^2+5+2=0

We add all the numbers together, and all the variables

20a/50a^2+15a/50a^2+7=0

We multiply all the terms by the denominator


20a+15a+7*50a^2=0

We add all the numbers together, and all the variables

35a+7*50a^2=0

Wy multiply elements

350a^2+35a=0

a = 350; b = 35; c = 0;
Δ = b2-4ac
Δ = 352-4·350·0
Δ = 1225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1225}=35$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(35)-35}{2*350}=\frac{-70}{700}
=-1/10
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(35)+35}{2*350}=\frac{0}{700}
=0
$