1/7x-4=-4x+2/7x+5

Solution for 1/7x-4=-4x+2/7x+5 equation:

1/7x-4=-4x+2/7x+5

We move all terms to the left:

1/7x-4-(-4x+2/7x+5)=0


Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R



Domain of the equation: 7x+5)!=0

x∈R


We get rid of parentheses

1/7x+4x-2/7x-5-4=0

We multiply all the terms by the denominator


4x*7x-5*7x-4*7x+1-2=0

We add all the numbers together, and all the variables

4x*7x-5*7x-4*7x-1=0

Wy multiply elements

28x^2-35x-28x-1=0

We add all the numbers together, and all the variables

28x^2-63x-1=0

a = 28; b = -63; c = -1;
Δ = b2-4ac
Δ = -632-4·28·(-1)
Δ = 4081
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{-(-63)-\sqrt{4081}}{2*28}=\frac{63-\sqrt{4081}}{56}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-63)+\sqrt{4081}}{2*28}=\frac{63+\sqrt{4081}}{56}
$