176.4=180x-360/x

Solution for 176.4=180x-360/x equation:

176.4=180x-360/x

We move all terms to the left:

176.4-(180x-360/x)=0


Domain of the equation: x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

-(+180x-360/x)+176.4=0

We get rid of parentheses

-180x+360/x+176.4=0

We multiply all the terms by the denominator


-180x*x+(176.4)*x+360=0

We multiply parentheses

-180x*x+176.4x+360=0

Wy multiply elements

-180x^2+176.4x+360=0

a = -180; b = 176.4; c = +360;
Δ = b2-4ac
Δ = 176.42-4·(-180)·360
Δ = 290316.96
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(176.4)-\sqrt{290316.96}}{2*-180}=\frac{-176.4-\sqrt{290316.96}}{-360}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(176.4)+\sqrt{290316.96}}{2*-180}=\frac{-176.4+\sqrt{290316.96}}{-360}
$