3/5a+-3=5a

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

3/5a+-3=5a

We move all terms to the left:

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


Domain of the equation: 5a!=0

a!=0/5

a!=0

a∈R


We add all the numbers together, and all the variables

-5a+3/5a=0

We multiply all the terms by the denominator


-5a*5a+3=0

Wy multiply elements

-25a^2+3=0

a = -25; b = 0; c = +3;
Δ = b2-4ac
Δ = 02-4·(-25)·3
Δ = 300
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{300}=\sqrt{100*3}=\sqrt{100}*\sqrt{3}=10\sqrt{3}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-10\sqrt{3}}{2*-25}=\frac{0-10\sqrt{3}}{-50}
=-\frac{10\sqrt{3}}{-50}
=-\frac{\sqrt{3}}{-5}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+10\sqrt{3}}{2*-25}=\frac{0+10\sqrt{3}}{-50}
=\frac{10\sqrt{3}}{-50}
=\frac{\sqrt{3}}{-5}
$