3x-4=1/29x-20

Solution for 3x-4=1/29x-20 equation:

3x-4=1/29x-20

We move all terms to the left:

3x-4-(1/29x-20)=0


Domain of the equation: 29x-20)!=0

x∈R


We get rid of parentheses

3x-1/29x+20-4=0

We multiply all the terms by the denominator


3x*29x+20*29x-4*29x-1=0

Wy multiply elements

87x^2+580x-116x-1=0

We add all the numbers together, and all the variables

87x^2+464x-1=0

a = 87; b = 464; c = -1;
Δ = b2-4ac
Δ = 4642-4·87·(-1)
Δ = 215644
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:

$\sqrt{\Delta}=\sqrt{215644}=\sqrt{676*319}=\sqrt{676}*\sqrt{319}=26\sqrt{319}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(464)-26\sqrt{319}}{2*87}=\frac{-464-26\sqrt{319}}{174}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(464)+26\sqrt{319}}{2*87}=\frac{-464+26\sqrt{319}}{174}
$