180=90+x+1/2x

Solution for 180=90+x+1/2x equation:

180=90+x+1/2x

We move all terms to the left:

180-(90+x+1/2x)=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+1/2x+90)+180=0

We get rid of parentheses

-x-1/2x-90+180=0

We multiply all the terms by the denominator


-x*2x-90*2x+180*2x-1=0

Wy multiply elements

-2x^2-180x+360x-1=0

We add all the numbers together, and all the variables

-2x^2+180x-1=0

a = -2; b = 180; c = -1;
Δ = b2-4ac
Δ = 1802-4·(-2)·(-1)
Δ = 32392
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:

$\sqrt{\Delta}=\sqrt{32392}=\sqrt{4*8098}=\sqrt{4}*\sqrt{8098}=2\sqrt{8098}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(180)-2\sqrt{8098}}{2*-2}=\frac{-180-2\sqrt{8098}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(180)+2\sqrt{8098}}{2*-2}=\frac{-180+2\sqrt{8098}}{-4}
$