5/2x-4=x+4

Solution for 5/2x-4=x+4 equation:

5/2x-4=x+4

We move all terms to the left:

5/2x-4-(x+4)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We get rid of parentheses

5/2x-x-4-4=0

We multiply all the terms by the denominator


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

Wy multiply elements

-2x^2-8x-8x+5=0

We add all the numbers together, and all the variables

-2x^2-16x+5=0

a = -2; b = -16; c = +5;
Δ = b2-4ac
Δ = -162-4·(-2)·5
Δ = 296
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:

$\sqrt{\Delta}=\sqrt{296}=\sqrt{4*74}=\sqrt{4}*\sqrt{74}=2\sqrt{74}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-2\sqrt{74}}{2*-2}=\frac{16-2\sqrt{74}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+2\sqrt{74}}{2*-2}=\frac{16+2\sqrt{74}}{-4}
$