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2x+1/2x=180
We move all terms to the left:
2x+1/2x-(180)=0
Domain of the equation: 2x!=0We multiply all the terms by the denominator
x!=0/2
x!=0
x∈R
2x*2x-180*2x+1=0
Wy multiply elements
4x^2-360x+1=0
a = 4; b = -360; c = +1;
Δ = b2-4ac
Δ = -3602-4·4·1
Δ = 129584
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{129584}=\sqrt{16*8099}=\sqrt{16}*\sqrt{8099}=4\sqrt{8099}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-360)-4\sqrt{8099}}{2*4}=\frac{360-4\sqrt{8099}}{8} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-360)+4\sqrt{8099}}{2*4}=\frac{360+4\sqrt{8099}}{8} $
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