25-1/3*x=2

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

25-1/3*x=2

We move all terms to the left:

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


Domain of the equation: 3*x!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

-1/3*x+23=0

We multiply all the terms by the denominator


23*3*x-1=0

Wy multiply elements

69x*x-1=0

Wy multiply elements

69x^2-1=0

a = 69; b = 0; c = -1;
Δ = b2-4ac
Δ = 02-4·69·(-1)
Δ = 276
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:

$\sqrt{\Delta}=\sqrt{276}=\sqrt{4*69}=\sqrt{4}*\sqrt{69}=2\sqrt{69}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{69}}{2*69}=\frac{0-2\sqrt{69}}{138}
=-\frac{2\sqrt{69}}{138}
=-\frac{\sqrt{69}}{69}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{69}}{2*69}=\frac{0+2\sqrt{69}}{138}
=\frac{2\sqrt{69}}{138}
=\frac{\sqrt{69}}{69}
$