2/a+3/2a=7

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

2/a+3/2a=7

We move all terms to the left:

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


Domain of the equation: a!=0

a∈R



Domain of the equation: 2a!=0

a!=0/2

a!=0

a∈R


We calculate fractions


4a/2a^2+3a/2a^2-7=0

We multiply all the terms by the denominator


4a+3a-7*2a^2=0

We add all the numbers together, and all the variables

7a-7*2a^2=0

Wy multiply elements

-14a^2+7a=0

a = -14; b = 7; c = 0;
Δ = b2-4ac
Δ = 72-4·(-14)·0
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-7}{2*-14}=\frac{-14}{-28}
=1/2
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+7}{2*-14}=\frac{0}{-28}
=0
$