5+x=18+4/5x

Solution for 5+x=18+4/5x equation:

5+x=18+4/5x

We move all terms to the left:

5+x-(18+4/5x)=0


Domain of the equation: 5x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

x-(4/5x+18)+5=0

We get rid of parentheses

x-4/5x-18+5=0

We multiply all the terms by the denominator


x*5x-18*5x+5*5x-4=0

Wy multiply elements

5x^2-90x+25x-4=0

We add all the numbers together, and all the variables

5x^2-65x-4=0

a = 5; b = -65; c = -4;
Δ = b2-4ac
Δ = -652-4·5·(-4)
Δ = 4305
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-65)-\sqrt{4305}}{2*5}=\frac{65-\sqrt{4305}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-65)+\sqrt{4305}}{2*5}=\frac{65+\sqrt{4305}}{10}
$