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1/2x+2x+5=100
We move all terms to the left:
1/2x+2x+5-(100)=0
Domain of the equation: 2x!=0We add all the numbers together, and all the variables
x!=0/2
x!=0
x∈R
2x+1/2x-95=0
We multiply all the terms by the denominator
2x*2x-95*2x+1=0
Wy multiply elements
4x^2-190x+1=0
a = 4; b = -190; c = +1;
Δ = b2-4ac
Δ = -1902-4·4·1
Δ = 36084
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{36084}=\sqrt{4*9021}=\sqrt{4}*\sqrt{9021}=2\sqrt{9021}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-190)-2\sqrt{9021}}{2*4}=\frac{190-2\sqrt{9021}}{8} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-190)+2\sqrt{9021}}{2*4}=\frac{190+2\sqrt{9021}}{8} $
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