X-1/3x=28

Solution for X-1/3x=28 equation:

X-1/3X=28

We move all terms to the left:

X-1/3X-(28)=0


Domain of the equation: 3X!=0

X!=0/3

X!=0

X∈R


We multiply all the terms by the denominator


X*3X-28*3X-1=0

Wy multiply elements

3X^2-84X-1=0

a = 3; b = -84; c = -1;
Δ = b2-4ac
Δ = -842-4·3·(-1)
Δ = 7068
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:

$\sqrt{\Delta}=\sqrt{7068}=\sqrt{4*1767}=\sqrt{4}*\sqrt{1767}=2\sqrt{1767}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-84)-2\sqrt{1767}}{2*3}=\frac{84-2\sqrt{1767}}{6}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-84)+2\sqrt{1767}}{2*3}=\frac{84+2\sqrt{1767}}{6}
$