x=41/39x+4

Solution for x=41/39x+4 equation:

x=41/39x+4

We move all terms to the left:

x-(41/39x+4)=0


Domain of the equation: 39x+4)!=0

x∈R


We get rid of parentheses

x-41/39x-4=0

We multiply all the terms by the denominator


x*39x-4*39x-41=0

Wy multiply elements

39x^2-156x-41=0

a = 39; b = -156; c = -41;
Δ = b2-4ac
Δ = -1562-4·39·(-41)
Δ = 30732
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:

$\sqrt{\Delta}=\sqrt{30732}=\sqrt{4*7683}=\sqrt{4}*\sqrt{7683}=2\sqrt{7683}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-156)-2\sqrt{7683}}{2*39}=\frac{156-2\sqrt{7683}}{78}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-156)+2\sqrt{7683}}{2*39}=\frac{156+2\sqrt{7683}}{78}
$