180-x=3/2x

Solution for 180-x=3/2x equation:

180-x=3/2x

We move all terms to the left:

180-x-(3/2x)=0


Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

-x-(+3/2x)+180=0

We add all the numbers together, and all the variables

-1x-(+3/2x)+180=0

We get rid of parentheses

-1x-3/2x+180=0

We multiply all the terms by the denominator


-1x*2x+180*2x-3=0

Wy multiply elements

-2x^2+360x-3=0

a = -2; b = 360; c = -3;
Δ = b2-4ac
Δ = 3602-4·(-2)·(-3)
Δ = 129576
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:

$\sqrt{\Delta}=\sqrt{129576}=\sqrt{4*32394}=\sqrt{4}*\sqrt{32394}=2\sqrt{32394}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(360)-2\sqrt{32394}}{2*-2}=\frac{-360-2\sqrt{32394}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(360)+2\sqrt{32394}}{2*-2}=\frac{-360+2\sqrt{32394}}{-4}
$