x=180-3/5x

Solution for x=180-3/5x equation:

x=180-3/5x

We move all terms to the left:

x-(180-3/5x)=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-(-3/5x+180)=0

We get rid of parentheses

x+3/5x-180=0

We multiply all the terms by the denominator


x*5x-180*5x+3=0

Wy multiply elements

5x^2-900x+3=0

a = 5; b = -900; c = +3;
Δ = b2-4ac
Δ = -9002-4·5·3
Δ = 809940
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:

$\sqrt{\Delta}=\sqrt{809940}=\sqrt{4*202485}=\sqrt{4}*\sqrt{202485}=2\sqrt{202485}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-900)-2\sqrt{202485}}{2*5}=\frac{900-2\sqrt{202485}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-900)+2\sqrt{202485}}{2*5}=\frac{900+2\sqrt{202485}}{10}
$