X+5/3x=68

Solution for X+5/3x=68 equation:

X+5/3X=68

We move all terms to the left:

X+5/3X-(68)=0


Domain of the equation: 3X!=0

X!=0/3

X!=0

X∈R


We multiply all the terms by the denominator


X*3X-68*3X+5=0

Wy multiply elements

3X^2-204X+5=0

a = 3; b = -204; c = +5;
Δ = b2-4ac
Δ = -2042-4·3·5
Δ = 41556
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:

$\sqrt{\Delta}=\sqrt{41556}=\sqrt{4*10389}=\sqrt{4}*\sqrt{10389}=2\sqrt{10389}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-204)-2\sqrt{10389}}{2*3}=\frac{204-2\sqrt{10389}}{6}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-204)+2\sqrt{10389}}{2*3}=\frac{204+2\sqrt{10389}}{6}
$