(1+2x)9=1-(x+4)/6

Solution for (1+2x)9=1-(x+4)/6 equation:

(1+2x)9=1-(x+4)/6

We move all terms to the left:

(1+2x)9-(1-(x+4)/6)=0

We add all the numbers together, and all the variables

(2x+1)9-(1-(x+4)/6)=0

We multiply parentheses

18x-(1-(x+4)/6)+9=0

We multiply all the terms by the denominator


18x*6)-(1-(x+4)+9*6)=0

We add all the numbers together, and all the variables

18x*6)-(1-(x+4)=0

Wy multiply elements

108x^2-(x+4)=0

We get rid of parentheses

108x^2-x-4=0

We add all the numbers together, and all the variables

108x^2-1x-4=0

a = 108; b = -1; c = -4;
Δ = b2-4ac
Δ = -12-4·108·(-4)
Δ = 1729
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-\sqrt{1729}}{2*108}=\frac{1-\sqrt{1729}}{216}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{1729}}{2*108}=\frac{1+\sqrt{1729}}{216}
$