2x-1/3x=-25

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

2x-1/3x=-25

We move all terms to the left:

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

We multiply all the terms by the denominator


2x*3x+25*3x-1=0

Wy multiply elements

6x^2+75x-1=0

a = 6; b = 75; c = -1;
Δ = b2-4ac
Δ = 752-4·6·(-1)
Δ = 5649
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(75)-\sqrt{5649}}{2*6}=\frac{-75-\sqrt{5649}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(75)+\sqrt{5649}}{2*6}=\frac{-75+\sqrt{5649}}{12}
$