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1x=8/6x-2
We move all terms to the left:
1x-(8/6x-2)=0
Domain of the equation: 6x-2)!=0We add all the numbers together, and all the variables
x∈R
x-(8/6x-2)=0
We get rid of parentheses
x-8/6x+2=0
We multiply all the terms by the denominator
x*6x+2*6x-8=0
Wy multiply elements
6x^2+12x-8=0
a = 6; b = 12; c = -8;
Δ = b2-4ac
Δ = 122-4·6·(-8)
Δ = 336
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{336}=\sqrt{16*21}=\sqrt{16}*\sqrt{21}=4\sqrt{21}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-4\sqrt{21}}{2*6}=\frac{-12-4\sqrt{21}}{12} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+4\sqrt{21}}{2*6}=\frac{-12+4\sqrt{21}}{12} $
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