(3/2)a+(3/4)a+(3/8)a=105

Solution for (3/2)a+(3/4)a+(3/8)a=105 equation:

(3/2)a+(3/4)a+(3/8)a=105

We move all terms to the left:

(3/2)a+(3/4)a+(3/8)a-(105)=0


Domain of the equation: 2)a!=0

a!=0/1

a!=0

a∈R



Domain of the equation: 4)a!=0

a!=0/1

a!=0

a∈R



Domain of the equation: 8)a!=0

a!=0/1

a!=0

a∈R


We add all the numbers together, and all the variables

(+3/2)a+(+3/4)a+(+3/8)a-105=0

We multiply parentheses

3a^2+3a^2+3a^2-105=0

We add all the numbers together, and all the variables

9a^2-105=0

a = 9; b = 0; c = -105;
Δ = b2-4ac
Δ = 02-4·9·(-105)
Δ = 3780
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:

$\sqrt{\Delta}=\sqrt{3780}=\sqrt{36*105}=\sqrt{36}*\sqrt{105}=6\sqrt{105}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{105}}{2*9}=\frac{0-6\sqrt{105}}{18}
=-\frac{6\sqrt{105}}{18}
=-\frac{\sqrt{105}}{3}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{105}}{2*9}=\frac{0+6\sqrt{105}}{18}
=\frac{6\sqrt{105}}{18}
=\frac{\sqrt{105}}{3}
$