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

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

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

We move all terms to the left:

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


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 4x+2x)!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

-2x*4x-7*4x-10=0

Wy multiply elements

-8x^2-28x-10=0

a = -8; b = -28; c = -10;
Δ = b2-4ac
Δ = -282-4·(-8)·(-10)
Δ = 464
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:

$\sqrt{\Delta}=\sqrt{464}=\sqrt{16*29}=\sqrt{16}*\sqrt{29}=4\sqrt{29}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-28)-4\sqrt{29}}{2*-8}=\frac{28-4\sqrt{29}}{-16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-28)+4\sqrt{29}}{2*-8}=\frac{28+4\sqrt{29}}{-16}
$