5x-28=1/3x

Solution for 5x-28=1/3x equation:

5x-28=1/3x

We move all terms to the left:

5x-28-(1/3x)=0


Domain of the equation: 3x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

5x-(+1/3x)-28=0

We get rid of parentheses

5x-1/3x-28=0

We multiply all the terms by the denominator


5x*3x-28*3x-1=0

Wy multiply elements

15x^2-84x-1=0

a = 15; b = -84; c = -1;
Δ = b2-4ac
Δ = -842-4·15·(-1)
Δ = 7116
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:

$\sqrt{\Delta}=\sqrt{7116}=\sqrt{4*1779}=\sqrt{4}*\sqrt{1779}=2\sqrt{1779}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-84)-2\sqrt{1779}}{2*15}=\frac{84-2\sqrt{1779}}{30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-84)+2\sqrt{1779}}{2*15}=\frac{84+2\sqrt{1779}}{30}
$