1/3x-25-2x=3

Solution for 1/3x-25-2x=3 equation:

1/3x-25-2x=3

We move all terms to the left:

1/3x-25-2x-(3)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

-2x+1/3x-28=0

We multiply all the terms by the denominator


-2x*3x-28*3x+1=0

Wy multiply elements

-6x^2-84x+1=0

a = -6; b = -84; c = +1;
Δ = b2-4ac
Δ = -842-4·(-6)·1
Δ = 7080
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:

$\sqrt{\Delta}=\sqrt{7080}=\sqrt{4*1770}=\sqrt{4}*\sqrt{1770}=2\sqrt{1770}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-84)-2\sqrt{1770}}{2*-6}=\frac{84-2\sqrt{1770}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-84)+2\sqrt{1770}}{2*-6}=\frac{84+2\sqrt{1770}}{-12}
$