3/5a-1/2a-3=17

Solution for 3/5a-1/2a-3=17 equation:

3/5a-1/2a-3=17

We move all terms to the left:

3/5a-1/2a-3-(17)=0


Domain of the equation: 5a!=0

a!=0/5

a!=0

a∈R



Domain of the equation: 2a!=0

a!=0/2

a!=0

a∈R


We add all the numbers together, and all the variables

3/5a-1/2a-20=0

We calculate fractions


6a/10a^2+(-5a)/10a^2-20=0

We multiply all the terms by the denominator


6a+(-5a)-20*10a^2=0

Wy multiply elements

-200a^2+6a+(-5a)=0

We get rid of parentheses

-200a^2+6a-5a=0

We add all the numbers together, and all the variables

-200a^2+a=0

a = -200; b = 1; c = 0;
Δ = b2-4ac
Δ = 12-4·(-200)·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-1}{2*-200}=\frac{-2}{-400}
=1/200
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+1}{2*-200}=\frac{0}{-400}
=0
$