1/2x+4x-5=8x-7/2x+9-14

Solution for 1/2x+4x-5=8x-7/2x+9-14 equation:

1/2x+4x-5=8x-7/2x+9-14

We move all terms to the left:

1/2x+4x-5-(8x-7/2x+9-14)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 2x+9-14)!=0

We move all terms containing x to the left, all other terms to the right

2x-14)!=-9

x∈R


We add all the numbers together, and all the variables

1/2x+4x-(8x-7/2x-5)-5=0

We add all the numbers together, and all the variables

4x+1/2x-(8x-7/2x-5)-5=0

We get rid of parentheses

4x+1/2x-8x+7/2x+5-5=0

We multiply all the terms by the denominator


4x*2x-8x*2x+5*2x-5*2x+1+7=0

We add all the numbers together, and all the variables

4x*2x-8x*2x+5*2x-5*2x+8=0

Wy multiply elements

8x^2-16x^2+10x-10x+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
$