5x-4/5x+4=2-3

Solution for 5x-4/5x+4=2-3 equation:

5x-4/5x+4=2-3

We move all terms to the left:

5x-4/5x+4-(2-3)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We add all the numbers together, and all the variables

5x-4/5x+4-(-1)=0

We add all the numbers together, and all the variables

5x-4/5x+5=0

We multiply all the terms by the denominator


5x*5x+5*5x-4=0

Wy multiply elements

25x^2+25x-4=0

a = 25; b = 25; c = -4;
Δ = b2-4ac
Δ = 252-4·25·(-4)
Δ = 1025
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1025}=\sqrt{25*41}=\sqrt{25}*\sqrt{41}=5\sqrt{41}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(25)-5\sqrt{41}}{2*25}=\frac{-25-5\sqrt{41}}{50}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(25)+5\sqrt{41}}{2*25}=\frac{-25+5\sqrt{41}}{50}
$