3x-1=1/28x-20

Solution for 3x-1=1/28x-20 equation:

3x-1=1/28x-20

We move all terms to the left:

3x-1-(1/28x-20)=0


Domain of the equation: 28x-20)!=0

x∈R


We get rid of parentheses

3x-1/28x+20-1=0

We multiply all the terms by the denominator


3x*28x+20*28x-1*28x-1=0

Wy multiply elements

84x^2+560x-28x-1=0

We add all the numbers together, and all the variables

84x^2+532x-1=0

a = 84; b = 532; c = -1;
Δ = b2-4ac
Δ = 5322-4·84·(-1)
Δ = 283360
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:

$\sqrt{\Delta}=\sqrt{283360}=\sqrt{16*17710}=\sqrt{16}*\sqrt{17710}=4\sqrt{17710}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(532)-4\sqrt{17710}}{2*84}=\frac{-532-4\sqrt{17710}}{168}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(532)+4\sqrt{17710}}{2*84}=\frac{-532+4\sqrt{17710}}{168}
$