x=2/5x+83

Solution for x=2/5x+83 equation:

x=2/5x+83

We move all terms to the left:

x-(2/5x+83)=0


Domain of the equation: 5x+83)!=0

x∈R


We get rid of parentheses

x-2/5x-83=0

We multiply all the terms by the denominator


x*5x-83*5x-2=0

Wy multiply elements

5x^2-415x-2=0

a = 5; b = -415; c = -2;
Δ = b2-4ac
Δ = -4152-4·5·(-2)
Δ = 172265
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{-(-415)-\sqrt{172265}}{2*5}=\frac{415-\sqrt{172265}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-415)+\sqrt{172265}}{2*5}=\frac{415+\sqrt{172265}}{10}
$