X-1/3x=80

Solution for X-1/3x=80 equation:

X-1/3X=80

We move all terms to the left:

X-1/3X-(80)=0


Domain of the equation: 3X!=0

X!=0/3

X!=0

X∈R


We multiply all the terms by the denominator


X*3X-80*3X-1=0

Wy multiply elements

3X^2-240X-1=0

a = 3; b = -240; c = -1;
Δ = b2-4ac
Δ = -2402-4·3·(-1)
Δ = 57612
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:

$\sqrt{\Delta}=\sqrt{57612}=\sqrt{4*14403}=\sqrt{4}*\sqrt{14403}=2\sqrt{14403}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-240)-2\sqrt{14403}}{2*3}=\frac{240-2\sqrt{14403}}{6}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-240)+2\sqrt{14403}}{2*3}=\frac{240+2\sqrt{14403}}{6}
$