x=3/5x+18

Solution for x=3/5x+18 equation:

x=3/5x+18

We move all terms to the left:

x-(3/5x+18)=0


Domain of the equation: 5x+18)!=0

x∈R


We get rid of parentheses

x-3/5x-18=0

We multiply all the terms by the denominator


x*5x-18*5x-3=0

Wy multiply elements

5x^2-90x-3=0

a = 5; b = -90; c = -3;
Δ = b2-4ac
Δ = -902-4·5·(-3)
Δ = 8160
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:

$\sqrt{\Delta}=\sqrt{8160}=\sqrt{16*510}=\sqrt{16}*\sqrt{510}=4\sqrt{510}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-90)-4\sqrt{510}}{2*5}=\frac{90-4\sqrt{510}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-90)+4\sqrt{510}}{2*5}=\frac{90+4\sqrt{510}}{10}
$