-1/4x-7+9/4x+2x=4x-7

Solution for -1/4x-7+9/4x+2x=4x-7 equation:

-1/4x-7+9/4x+2x=4x-7

We move all terms to the left:

-1/4x-7+9/4x+2x-(4x-7)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We add all the numbers together, and all the variables

2x-1/4x+9/4x-(4x-7)-7=0

We get rid of parentheses

2x-1/4x+9/4x-4x+7-7=0

We multiply all the terms by the denominator


2x*4x-4x*4x+7*4x-7*4x-1+9=0

We add all the numbers together, and all the variables

2x*4x-4x*4x+7*4x-7*4x+8=0

Wy multiply elements

8x^2-16x^2+28x-28x+8=0

We add all the numbers together, and all the variables

-8x^2+8=0

a = -8; b = 0; c = +8;
Δ = b2-4ac
Δ = 02-4·(-8)·8
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-16}{2*-8}=\frac{-16}{-16}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+16}{2*-8}=\frac{16}{-16}
=-1
$