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90-x+5/2x=180
We move all terms to the left:
90-x+5/2x-(180)=0
Domain of the equation: 2x!=0We add all the numbers together, and all the variables
x!=0/2
x!=0
x∈R
-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} $
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