4x-(1/9)(-81x+18)+12=63

Solution for 4x-(1/9)(-81x+18)+12=63 equation:

4x-(1/9)(-81x+18)+12=63

We move all terms to the left:

4x-(1/9)(-81x+18)+12-(63)=0


Domain of the equation: 9)(-81x+18)!=0

x∈R


We add all the numbers together, and all the variables

4x-(+1/9)(-81x+18)+12-63=0

We add all the numbers together, and all the variables

4x-(+1/9)(-81x+18)-51=0

We multiply parentheses ..

-(-81x^2+1/9*18)+4x-51=0

We multiply all the terms by the denominator


-(-81x^2+1+4x*9*18)-51*9*18)=0

We add all the numbers together, and all the variables

-(-81x^2+1+4x*9*18)=0

We get rid of parentheses

81x^2-4x*9*18-1=0

Wy multiply elements

81x^2-648x*1-1=0

Wy multiply elements

81x^2-648x-1=0

a = 81; b = -648; c = -1;
Δ = b2-4ac
Δ = -6482-4·81·(-1)
Δ = 420228
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:

$\sqrt{\Delta}=\sqrt{420228}=\sqrt{324*1297}=\sqrt{324}*\sqrt{1297}=18\sqrt{1297}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-648)-18\sqrt{1297}}{2*81}=\frac{648-18\sqrt{1297}}{162}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-648)+18\sqrt{1297}}{2*81}=\frac{648+18\sqrt{1297}}{162}
$