1.3a+1=1/2a

Solution for 1.3a+1=1/2a equation:

1.3a+1=1/2a

We move all terms to the left:

1.3a+1-(1/2a)=0


Domain of the equation: 2a)!=0

a!=0/1

a!=0

a∈R


We add all the numbers together, and all the variables

1.3a-(+1/2a)+1=0

We get rid of parentheses

1.3a-1/2a+1=0

We multiply all the terms by the denominator


(1.3a)*2a+1*2a-1=0

We add all the numbers together, and all the variables

(+1.3a)*2a+1*2a-1=0

We multiply parentheses

2a^2+1*2a-1=0

Wy multiply elements

2a^2+2a-1=0

a = 2; b = 2; c = -1;
Δ = b2-4ac
Δ = 22-4·2·(-1)
Δ = 12
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:

$\sqrt{\Delta}=\sqrt{12}=\sqrt{4*3}=\sqrt{4}*\sqrt{3}=2\sqrt{3}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{3}}{2*2}=\frac{-2-2\sqrt{3}}{4}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{3}}{2*2}=\frac{-2+2\sqrt{3}}{4}
$