3/5a+a=4

Solution for 3/5a+a=4 equation:

3/5a+a=4

We move all terms to the left:

3/5a+a-(4)=0


Domain of the equation: 5a!=0

a!=0/5

a!=0

a∈R


We add all the numbers together, and all the variables

a+3/5a-4=0

We multiply all the terms by the denominator


a*5a-4*5a+3=0

Wy multiply elements

5a^2-20a+3=0

a = 5; b = -20; c = +3;
Δ = b2-4ac
Δ = -202-4·5·3
Δ = 340
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:

$\sqrt{\Delta}=\sqrt{340}=\sqrt{4*85}=\sqrt{4}*\sqrt{85}=2\sqrt{85}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-2\sqrt{85}}{2*5}=\frac{20-2\sqrt{85}}{10}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+2\sqrt{85}}{2*5}=\frac{20+2\sqrt{85}}{10}
$