2/5a-3=3/1-a-2

Solution for 2/5a-3=3/1-a-2 equation:

2/5a-3=3/1-a-2

We move all terms to the left:

2/5a-3-(3/1-a-2)=0


Domain of the equation: 5a!=0

a!=0/5

a!=0

a∈R



Domain of the equation: 1-a-2)!=0

We move all terms containing a to the left, all other terms to the right

-a-2)!=-1

a∈R


We add all the numbers together, and all the variables

2/5a-(-1a)-3=0

We get rid of parentheses

2/5a+1a-3=0

We multiply all the terms by the denominator


1a*5a-3*5a+2=0

Wy multiply elements

5a^2-15a+2=0

a = 5; b = -15; c = +2;
Δ = b2-4ac
Δ = -152-4·5·2
Δ = 185
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-\sqrt{185}}{2*5}=\frac{15-\sqrt{185}}{10}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+\sqrt{185}}{2*5}=\frac{15+\sqrt{185}}{10}
$