x=3/42x+1

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Solution for x=3/42x+1 equation:



x=3/42x+1
We move all terms to the left:
x-(3/42x+1)=0
Domain of the equation: 42x+1)!=0
x∈R
We get rid of parentheses
x-3/42x-1=0
We multiply all the terms by the denominator
x*42x-1*42x-3=0
Wy multiply elements
42x^2-42x-3=0
a = 42; b = -42; c = -3;
Δ = b2-4ac
Δ = -422-4·42·(-3)
Δ = 2268
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:
$\sqrt{\Delta}=\sqrt{2268}=\sqrt{324*7}=\sqrt{324}*\sqrt{7}=18\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-42)-18\sqrt{7}}{2*42}=\frac{42-18\sqrt{7}}{84} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-42)+18\sqrt{7}}{2*42}=\frac{42+18\sqrt{7}}{84} $

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