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2x+1/2x=60
We move all terms to the left:
2x+1/2x-(60)=0
Domain of the equation: 2x!=0We multiply all the terms by the denominator
x!=0/2
x!=0
x∈R
2x*2x-60*2x+1=0
Wy multiply elements
4x^2-120x+1=0
a = 4; b = -120; c = +1;
Δ = b2-4ac
Δ = -1202-4·4·1
Δ = 14384
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{14384}=\sqrt{16*899}=\sqrt{16}*\sqrt{899}=4\sqrt{899}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-120)-4\sqrt{899}}{2*4}=\frac{120-4\sqrt{899}}{8} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-120)+4\sqrt{899}}{2*4}=\frac{120+4\sqrt{899}}{8} $
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