5/2x+2=x-4

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

5/2x+2=x-4

We move all terms to the left:

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

We multiply all the terms by the denominator


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

Wy multiply elements

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

We add all the numbers together, and all the variables

-2x^2+12x+5=0

a = -2; b = 12; c = +5;
Δ = b2-4ac
Δ = 122-4·(-2)·5
Δ = 184
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:

$\sqrt{\Delta}=\sqrt{184}=\sqrt{4*46}=\sqrt{4}*\sqrt{46}=2\sqrt{46}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-2\sqrt{46}}{2*-2}=\frac{-12-2\sqrt{46}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+2\sqrt{46}}{2*-2}=\frac{-12+2\sqrt{46}}{-4}
$