3x-8/5x+8=1

Solution for 3x-8/5x+8=1 equation:

3x-8/5x+8=1

We move all terms to the left:

3x-8/5x+8-(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

3x-8/5x+7=0

We multiply all the terms by the denominator


3x*5x+7*5x-8=0

Wy multiply elements

15x^2+35x-8=0

a = 15; b = 35; c = -8;
Δ = b2-4ac
Δ = 352-4·15·(-8)
Δ = 1705
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{-(35)-\sqrt{1705}}{2*15}=\frac{-35-\sqrt{1705}}{30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(35)+\sqrt{1705}}{2*15}=\frac{-35+\sqrt{1705}}{30}
$