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)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

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

Wy multiply elements

8x^2-16x^2-10x+8=0

We add all the numbers together, and all the variables

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

a = -8; b = -10; c = +8;
Δ = b2-4ac
Δ = -102-4·(-8)·8
Δ = 356
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:

$\sqrt{\Delta}=\sqrt{356}=\sqrt{4*89}=\sqrt{4}*\sqrt{89}=2\sqrt{89}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{89}}{2*-8}=\frac{10-2\sqrt{89}}{-16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{89}}{2*-8}=\frac{10+2\sqrt{89}}{-16}
$