15/a^-1=5/2a-2

Solution for 15/a^-1=5/2a-2 equation:

15/a^-1=5/2a-2

We move all terms to the left:

15/a^-1-(5/2a-2)=0


Domain of the equation: a^!=0

a!=0/1

a!=0

a∈R



Domain of the equation: 2a-2)!=0

a∈R


We get rid of parentheses

15/a^-5/2a+2-1=0

We calculate fractions


30a/2a^2+(-5a)/2a^2+2-1=0

We add all the numbers together, and all the variables

30a/2a^2+(-5a)/2a^2+1=0

We multiply all the terms by the denominator


30a+(-5a)+1*2a^2=0

Wy multiply elements

2a^2+30a+(-5a)=0

We get rid of parentheses

2a^2+30a-5a=0

We add all the numbers together, and all the variables

2a^2+25a=0

a = 2; b = 25; c = 0;
Δ = b2-4ac
Δ = 252-4·2·0
Δ = 625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{625}=25$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(25)-25}{2*2}=\frac{-50}{4}
=-12+1/2
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(25)+25}{2*2}=\frac{0}{4}
=0
$