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176.4=180x-360/x
We move all terms to the left:
176.4-(180x-360/x)=0
Domain of the equation: x)!=0We add all the numbers together, and all the variables
x!=0/1
x!=0
x∈R
-(+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} $
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