-2a+3/a+1=-1

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

-2a+3/a+1=-1

We move all terms to the left:

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


Domain of the equation: a!=0

a∈R


We add all the numbers together, and all the variables

-2a+3/a+2=0

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

2a-2a*a+3=0

Wy multiply elements

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

a = -2; b = 2; c = +3;
Δ = b2-4ac
Δ = 22-4·(-2)·3
Δ = 28
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:

$\sqrt{\Delta}=\sqrt{28}=\sqrt{4*7}=\sqrt{4}*\sqrt{7}=2\sqrt{7}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{7}}{2*-2}=\frac{-2-2\sqrt{7}}{-4}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{7}}{2*-2}=\frac{-2+2\sqrt{7}}{-4}
$