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6x-19/6x-19=5
We move all terms to the left:
6x-19/6x-19-(5)=0
Domain of the equation: 6x!=0We add all the numbers together, and all the variables
x!=0/6
x!=0
x∈R
6x-19/6x-24=0
We multiply all the terms by the denominator
6x*6x-24*6x-19=0
Wy multiply elements
36x^2-144x-19=0
a = 36; b = -144; c = -19;
Δ = b2-4ac
Δ = -1442-4·36·(-19)
Δ = 23472
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{23472}=\sqrt{144*163}=\sqrt{144}*\sqrt{163}=12\sqrt{163}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-144)-12\sqrt{163}}{2*36}=\frac{144-12\sqrt{163}}{72} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-144)+12\sqrt{163}}{2*36}=\frac{144+12\sqrt{163}}{72} $
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