(10x+8/x)+18=10*8/x+x

Solution for (10x+8/x)+18=10*8/x+x equation:

(10x+8/x)+18=10*8/x+x

We move all terms to the left:

(10x+8/x)+18-(10*8/x+x)=0


Domain of the equation: x)!=0

x!=0/1

x!=0

x∈R



Domain of the equation: x+x)!=0

x∈R


We add all the numbers together, and all the variables

(+10x+8/x)-(+x+10*8/x)+18=0

We get rid of parentheses

10x+8/x-x-10*8/x+18=0

We multiply all the terms by the denominator


10x*x-x*x+18*x+8-10*8=0

We add all the numbers together, and all the variables

18x+10x*x-x*x-72=0

Wy multiply elements

10x^2-1x^2+18x-72=0

We add all the numbers together, and all the variables

9x^2+18x-72=0

a = 9; b = 18; c = -72;
Δ = b2-4ac
Δ = 182-4·9·(-72)
Δ = 2916
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2916}=54$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-54}{2*9}=\frac{-72}{18}
=-4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+54}{2*9}=\frac{36}{18}
=2
$