2x+8/5x-4=82

Solution for 2x+8/5x-4=82 equation:

2x+8/5x-4=82

We move all terms to the left:

2x+8/5x-4-(82)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We add all the numbers together, and all the variables

2x+8/5x-86=0

We multiply all the terms by the denominator


2x*5x-86*5x+8=0

Wy multiply elements

10x^2-430x+8=0

a = 10; b = -430; c = +8;
Δ = b2-4ac
Δ = -4302-4·10·8
Δ = 184580
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:

$\sqrt{\Delta}=\sqrt{184580}=\sqrt{4*46145}=\sqrt{4}*\sqrt{46145}=2\sqrt{46145}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-430)-2\sqrt{46145}}{2*10}=\frac{430-2\sqrt{46145}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-430)+2\sqrt{46145}}{2*10}=\frac{430+2\sqrt{46145}}{20}
$