5/3x=x+80

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

5/3x=x+80

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We get rid of parentheses

5/3x-x-80=0

We multiply all the terms by the denominator


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

Wy multiply elements

-3x^2-240x+5=0

a = -3; b = -240; c = +5;
Δ = b2-4ac
Δ = -2402-4·(-3)·5
Δ = 57660
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:

$\sqrt{\Delta}=\sqrt{57660}=\sqrt{3844*15}=\sqrt{3844}*\sqrt{15}=62\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-240)-62\sqrt{15}}{2*-3}=\frac{240-62\sqrt{15}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-240)+62\sqrt{15}}{2*-3}=\frac{240+62\sqrt{15}}{-6}
$