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2x+1+x+5/2x+3=180
We move all terms to the left:
2x+1+x+5/2x+3-(180)=0
Domain of the equation: 2x!=0We add all the numbers together, and all the variables
x!=0/2
x!=0
x∈R
3x+5/2x-176=0
We multiply all the terms by the denominator
3x*2x-176*2x+5=0
Wy multiply elements
6x^2-352x+5=0
a = 6; b = -352; c = +5;
Δ = b2-4ac
Δ = -3522-4·6·5
Δ = 123784
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{123784}=\sqrt{4*30946}=\sqrt{4}*\sqrt{30946}=2\sqrt{30946}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-352)-2\sqrt{30946}}{2*6}=\frac{352-2\sqrt{30946}}{12} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-352)+2\sqrt{30946}}{2*6}=\frac{352+2\sqrt{30946}}{12} $
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