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

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

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

We move all terms to the left:

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


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

28x^2-8x+8x-1=0

We add all the numbers together, and all the variables

28x^2-1=0

a = 28; b = 0; c = -1;
Δ = b2-4ac
Δ = 02-4·28·(-1)
Δ = 112
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:

$\sqrt{\Delta}=\sqrt{112}=\sqrt{16*7}=\sqrt{16}*\sqrt{7}=4\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{7}}{2*28}=\frac{0-4\sqrt{7}}{56}
=-\frac{4\sqrt{7}}{56}
=-\frac{\sqrt{7}}{14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{7}}{2*28}=\frac{0+4\sqrt{7}}{56}
=\frac{4\sqrt{7}}{56}
=\frac{\sqrt{7}}{14}
$