2a/a+2a=5a-48.

Solution for 2a/a+2a=5a-48. equation:

2a/a+2a=5a-48.

We move all terms to the left:

2a/a+2a-(5a-48.)=0


Domain of the equation: a!=0

a∈R


We add all the numbers together, and all the variables

2a/a+2a-(5a-48)=0

We add all the numbers together, and all the variables

2a+2a/a-(5a-48)=0

We get rid of parentheses

2a+2a/a-5a+48=0

We multiply all the terms by the denominator


2a*a+2a-5a*a+48*a=0

We add all the numbers together, and all the variables

50a+2a*a-5a*a=0

Wy multiply elements

2a^2-5a^2+50a=0

We add all the numbers together, and all the variables

-3a^2+50a=0

a = -3; b = 50; c = 0;
Δ = b2-4ac
Δ = 502-4·(-3)·0
Δ = 2500
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2500}=50$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(50)-50}{2*-3}=\frac{-100}{-6}
=16+2/3
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(50)+50}{2*-3}=\frac{0}{-6}
=0
$