2x-4=4/7x+1

Solution for 2x-4=4/7x+1 equation:

2x-4=4/7x+1

We move all terms to the left:

2x-4-(4/7x+1)=0


Domain of the equation: 7x+1)!=0

x∈R


We get rid of parentheses

2x-4/7x-1-4=0

We multiply all the terms by the denominator


2x*7x-1*7x-4*7x-4=0

Wy multiply elements

14x^2-7x-28x-4=0

We add all the numbers together, and all the variables

14x^2-35x-4=0

a = 14; b = -35; c = -4;
Δ = b2-4ac
Δ = -352-4·14·(-4)
Δ = 1449
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:

$\sqrt{\Delta}=\sqrt{1449}=\sqrt{9*161}=\sqrt{9}*\sqrt{161}=3\sqrt{161}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-35)-3\sqrt{161}}{2*14}=\frac{35-3\sqrt{161}}{28}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-35)+3\sqrt{161}}{2*14}=\frac{35+3\sqrt{161}}{28}
$