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(1/2x)(x)=162
We move all terms to the left:
(1/2x)(x)-(162)=0
Domain of the equation: 2x)x!=0We add all the numbers together, and all the variables
x!=0/1
x!=0
x∈R
(+1/2x)x-162=0
We multiply parentheses
x^2-162=0
a = 1; b = 0; c = -162;
Δ = b2-4ac
Δ = 02-4·1·(-162)
Δ = 648
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{648}=\sqrt{324*2}=\sqrt{324}*\sqrt{2}=18\sqrt{2}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-18\sqrt{2}}{2*1}=\frac{0-18\sqrt{2}}{2} =-\frac{18\sqrt{2}}{2} =-9\sqrt{2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+18\sqrt{2}}{2*1}=\frac{0+18\sqrt{2}}{2} =\frac{18\sqrt{2}}{2} =9\sqrt{2} $
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