x=3/42x+1

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}
$