5/2x+5/2x=18-x

Solution for 5/2x+5/2x=18-x equation:

5/2x+5/2x=18-x

We move all terms to the left:

5/2x+5/2x-(18-x)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

5/2x+5/2x-(-1x+18)=0

We get rid of parentheses

5/2x+5/2x+1x-18=0

We multiply all the terms by the denominator


1x*2x-18*2x+5+5=0

We add all the numbers together, and all the variables

1x*2x-18*2x+10=0

Wy multiply elements

2x^2-36x+10=0

a = 2; b = -36; c = +10;
Δ = b2-4ac
Δ = -362-4·2·10
Δ = 1216
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:

$\sqrt{\Delta}=\sqrt{1216}=\sqrt{64*19}=\sqrt{64}*\sqrt{19}=8\sqrt{19}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-8\sqrt{19}}{2*2}=\frac{36-8\sqrt{19}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+8\sqrt{19}}{2*2}=\frac{36+8\sqrt{19}}{4}
$