3/5x=x+16

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

3/5x=x+16

We move all terms to the left:

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


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We get rid of parentheses

3/5x-x-16=0

We multiply all the terms by the denominator


-x*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 = 6460
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:

$\sqrt{\Delta}=\sqrt{6460}=\sqrt{4*1615}=\sqrt{4}*\sqrt{1615}=2\sqrt{1615}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-80)-2\sqrt{1615}}{2*-5}=\frac{80-2\sqrt{1615}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-80)+2\sqrt{1615}}{2*-5}=\frac{80+2\sqrt{1615}}{-10}
$