7/2a+3/a=5

Solution for 7/2a+3/a=5 equation:

7/2a+3/a=5

We move all terms to the left:

7/2a+3/a-(5)=0


Domain of the equation: 2a!=0

a!=0/2

a!=0

a∈R



Domain of the equation: a!=0

a∈R


We calculate fractions


7a/2a^2+6a/2a^2-5=0

We multiply all the terms by the denominator


7a+6a-5*2a^2=0

We add all the numbers together, and all the variables

13a-5*2a^2=0

Wy multiply elements

-10a^2+13a=0

a = -10; b = 13; c = 0;
Δ = b2-4ac
Δ = 132-4·(-10)·0
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(13)-13}{2*-10}=\frac{-26}{-20}
=1+3/10
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+13}{2*-10}=\frac{0}{-20}
=0
$