4a-3/a+4=2a-1/a+2

Solution for 4a-3/a+4=2a-1/a+2 equation:

4a-3/a+4=2a-1/a+2

We move all terms to the left:

4a-3/a+4-(2a-1/a+2)=0


Domain of the equation: a!=0

a∈R



Domain of the equation: a+2)!=0

a∈R


We get rid of parentheses

4a-3/a-2a+1/a-2+4=0

We multiply all the terms by the denominator


4a*a-2a*a-2*a+4*a-3+1=0

We add all the numbers together, and all the variables

2a+4a*a-2a*a-2=0

Wy multiply elements

4a^2-2a^2+2a-2=0

We add all the numbers together, and all the variables

2a^2+2a-2=0

a = 2; b = 2; c = -2;
Δ = b2-4ac
Δ = 22-4·2·(-2)
Δ = 20
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:

$\sqrt{\Delta}=\sqrt{20}=\sqrt{4*5}=\sqrt{4}*\sqrt{5}=2\sqrt{5}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{5}}{2*2}=\frac{-2-2\sqrt{5}}{4}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{5}}{2*2}=\frac{-2+2\sqrt{5}}{4}
$