2/5*a=5

Solution for 2/5*a=5 equation:

2/5*a=5

We move all terms to the left:

2/5*a-(5)=0


Domain of the equation: 5*a!=0

a!=0/1

a!=0

a∈R


We multiply all the terms by the denominator


-5*5*a+2=0

Wy multiply elements

-25a*a+2=0

Wy multiply elements

-25a^2+2=0

a = -25; b = 0; c = +2;
Δ = b2-4ac
Δ = 02-4·(-25)·2
Δ = 200
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:

$\sqrt{\Delta}=\sqrt{200}=\sqrt{100*2}=\sqrt{100}*\sqrt{2}=10\sqrt{2}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-10\sqrt{2}}{2*-25}=\frac{0-10\sqrt{2}}{-50}
=-\frac{10\sqrt{2}}{-50}
=-\frac{\sqrt{2}}{-5}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+10\sqrt{2}}{2*-25}=\frac{0+10\sqrt{2}}{-50}
=\frac{10\sqrt{2}}{-50}
=\frac{\sqrt{2}}{-5}
$