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11/2x+23x=37
We move all terms to the left:
11/2x+23x-(37)=0
Domain of the equation: 2x!=0We add all the numbers together, and all the variables
x!=0/2
x!=0
x∈R
23x+11/2x-37=0
We multiply all the terms by the denominator
23x*2x-37*2x+11=0
Wy multiply elements
46x^2-74x+11=0
a = 46; b = -74; c = +11;
Δ = b2-4ac
Δ = -742-4·46·11
Δ = 3452
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{3452}=\sqrt{4*863}=\sqrt{4}*\sqrt{863}=2\sqrt{863}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-74)-2\sqrt{863}}{2*46}=\frac{74-2\sqrt{863}}{92} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-74)+2\sqrt{863}}{2*46}=\frac{74+2\sqrt{863}}{92} $
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