8+7/4x=-7/4x-2x

Solution for 8+7/4x=-7/4x-2x equation:

8+7/4x=-7/4x-2x

We move all terms to the left:

8+7/4x-(-7/4x-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

7/4x-(-2x-7/4x)+8=0

We get rid of parentheses

7/4x+2x+7/4x+8=0

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

2x*4x+8*4x+14=0

Wy multiply elements

8x^2+32x+14=0

a = 8; b = 32; c = +14;
Δ = b2-4ac
Δ = 322-4·8·14
Δ = 576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{576}=24$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(32)-24}{2*8}=\frac{-56}{16}
=-3+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(32)+24}{2*8}=\frac{-8}{16}
=-1/2
$