x+5/3x=56

Solution for x+5/3x=56 equation:

x+5/3x=56

We move all terms to the left:

x+5/3x-(56)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We multiply all the terms by the denominator


x*3x-56*3x+5=0

Wy multiply elements

3x^2-168x+5=0

a = 3; b = -168; c = +5;
Δ = b2-4ac
Δ = -1682-4·3·5
Δ = 28164
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:

$\sqrt{\Delta}=\sqrt{28164}=\sqrt{4*7041}=\sqrt{4}*\sqrt{7041}=2\sqrt{7041}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-168)-2\sqrt{7041}}{2*3}=\frac{168-2\sqrt{7041}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-168)+2\sqrt{7041}}{2*3}=\frac{168+2\sqrt{7041}}{6}
$