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10+20/2x+4x=47
We move all terms to the left:
10+20/2x+4x-(47)=0
Domain of the equation: 2x!=0We add all the numbers together, and all the variables
x!=0/2
x!=0
x∈R
4x+20/2x-37=0
We multiply all the terms by the denominator
4x*2x-37*2x+20=0
Wy multiply elements
8x^2-74x+20=0
a = 8; b = -74; c = +20;
Δ = b2-4ac
Δ = -742-4·8·20
Δ = 4836
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{4836}=\sqrt{4*1209}=\sqrt{4}*\sqrt{1209}=2\sqrt{1209}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-74)-2\sqrt{1209}}{2*8}=\frac{74-2\sqrt{1209}}{16} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-74)+2\sqrt{1209}}{2*8}=\frac{74+2\sqrt{1209}}{16} $
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