3/5x+80=x

Solution for 3/5x+80=x equation:

3/5x+80=x

We move all terms to the left:

3/5x+80-(x)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We add all the numbers together, and all the variables

-1x+3/5x+80=0

We multiply all the terms by the denominator


-1x*5x+80*5x+3=0

Wy multiply elements

-5x^2+400x+3=0

a = -5; b = 400; c = +3;
Δ = b2-4ac
Δ = 4002-4·(-5)·3
Δ = 160060
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:

$\sqrt{\Delta}=\sqrt{160060}=\sqrt{4*40015}=\sqrt{4}*\sqrt{40015}=2\sqrt{40015}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(400)-2\sqrt{40015}}{2*-5}=\frac{-400-2\sqrt{40015}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(400)+2\sqrt{40015}}{2*-5}=\frac{-400+2\sqrt{40015}}{-10}
$