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2x+1/6x-5=7
We move all terms to the left:
2x+1/6x-5-(7)=0
Domain of the equation: 6x!=0We add all the numbers together, and all the variables
x!=0/6
x!=0
x∈R
2x+1/6x-12=0
We multiply all the terms by the denominator
2x*6x-12*6x+1=0
Wy multiply elements
12x^2-72x+1=0
a = 12; b = -72; c = +1;
Δ = b2-4ac
Δ = -722-4·12·1
Δ = 5136
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{5136}=\sqrt{16*321}=\sqrt{16}*\sqrt{321}=4\sqrt{321}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-72)-4\sqrt{321}}{2*12}=\frac{72-4\sqrt{321}}{24} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-72)+4\sqrt{321}}{2*12}=\frac{72+4\sqrt{321}}{24} $
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