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150+30x=1/2x
We move all terms to the left:
150+30x-(1/2x)=0
Domain of the equation: 2x)!=0We add all the numbers together, and all the variables
x!=0/1
x!=0
x∈R
30x-(+1/2x)+150=0
We get rid of parentheses
30x-1/2x+150=0
We multiply all the terms by the denominator
30x*2x+150*2x-1=0
Wy multiply elements
60x^2+300x-1=0
a = 60; b = 300; c = -1;
Δ = b2-4ac
Δ = 3002-4·60·(-1)
Δ = 90240
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{90240}=\sqrt{64*1410}=\sqrt{64}*\sqrt{1410}=8\sqrt{1410}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(300)-8\sqrt{1410}}{2*60}=\frac{-300-8\sqrt{1410}}{120} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(300)+8\sqrt{1410}}{2*60}=\frac{-300+8\sqrt{1410}}{120} $
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