x+8/5x=85

Solution for x+8/5x=85 equation:

x+8/5x=85

We move all terms to the left:

x+8/5x-(85)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We multiply all the terms by the denominator


x*5x-85*5x+8=0

Wy multiply elements

5x^2-425x+8=0

a = 5; b = -425; c = +8;
Δ = b2-4ac
Δ = -4252-4·5·8
Δ = 180465
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{-(-425)-\sqrt{180465}}{2*5}=\frac{425-\sqrt{180465}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-425)+\sqrt{180465}}{2*5}=\frac{425+\sqrt{180465}}{10}
$