90-x+5/2x=180

Solution for 90-x+5/2x=180 equation:

90-x+5/2x=180

We move all terms to the left:

90-x+5/2x-(180)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

-1x+5/2x-90=0

We multiply all the terms by the denominator


-1x*2x-90*2x+5=0

Wy multiply elements

-2x^2-180x+5=0

a = -2; b = -180; c = +5;
Δ = b2-4ac
Δ = -1802-4·(-2)·5
Δ = 32440
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:

$\sqrt{\Delta}=\sqrt{32440}=\sqrt{4*8110}=\sqrt{4}*\sqrt{8110}=2\sqrt{8110}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-180)-2\sqrt{8110}}{2*-2}=\frac{180-2\sqrt{8110}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-180)+2\sqrt{8110}}{2*-2}=\frac{180+2\sqrt{8110}}{-4}
$