-2a+3/a+1=0

Solution for -2a+3/a+1=0 equation:

-2a+3/a+1=0


Domain of the equation: a!=0

a∈R


We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

a-2a*a+3=0

Wy multiply elements

-2a^2+a+3=0

a = -2; b = 1; c = +3;
Δ = b2-4ac
Δ = 12-4·(-2)·3
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-5}{2*-2}=\frac{-6}{-4}
=1+1/2
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+5}{2*-2}=\frac{4}{-4}
=-1
$