4x-8/5x+2=1

Solution for 4x-8/5x+2=1 equation:

4x-8/5x+2=1

We move all terms to the left:

4x-8/5x+2-(1)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We add all the numbers together, and all the variables

4x-8/5x+1=0

We multiply all the terms by the denominator


4x*5x+1*5x-8=0

Wy multiply elements

20x^2+5x-8=0

a = 20; b = 5; c = -8;
Δ = b2-4ac
Δ = 52-4·20·(-8)
Δ = 665
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-\sqrt{665}}{2*20}=\frac{-5-\sqrt{665}}{40}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{665}}{2*20}=\frac{-5+\sqrt{665}}{40}
$