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5/2x+2x=18
We move all terms to the left:
5/2x+2x-(18)=0
Domain of the equation: 2x!=0We add all the numbers together, and all the variables
x!=0/2
x!=0
x∈R
2x+5/2x-18=0
We multiply all the terms by the denominator
2x*2x-18*2x+5=0
Wy multiply elements
4x^2-36x+5=0
a = 4; b = -36; c = +5;
Δ = b2-4ac
Δ = -362-4·4·5
Δ = 1216
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{1216}=\sqrt{64*19}=\sqrt{64}*\sqrt{19}=8\sqrt{19}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-8\sqrt{19}}{2*4}=\frac{36-8\sqrt{19}}{8} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+8\sqrt{19}}{2*4}=\frac{36+8\sqrt{19}}{8} $
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