16-3/5x=x

Solution for 16-3/5x=x equation:

16-3/5x=x

We move all terms to the left:

16-3/5x-(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+16=0

We multiply all the terms by the denominator


-1x*5x+16*5x-3=0

Wy multiply elements

-5x^2+80x-3=0

a = -5; b = 80; c = -3;
Δ = b2-4ac
Δ = 802-4·(-5)·(-3)
Δ = 6340
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:

$\sqrt{\Delta}=\sqrt{6340}=\sqrt{4*1585}=\sqrt{4}*\sqrt{1585}=2\sqrt{1585}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(80)-2\sqrt{1585}}{2*-5}=\frac{-80-2\sqrt{1585}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(80)+2\sqrt{1585}}{2*-5}=\frac{-80+2\sqrt{1585}}{-10}
$