-(1/4)(12x+4)=x-9

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

-(1/4)(12x+4)=x-9

We move all terms to the left:

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


Domain of the equation: 4)(12x+4)!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We multiply parentheses ..

-(+12x^2+1/4*4)-x+9=0

We multiply all the terms by the denominator


-(+12x^2+1-x*4*4)+9*4*4)=0

We add all the numbers together, and all the variables

-(+12x^2+1-x*4*4)=0

We get rid of parentheses

-12x^2+x*4*4-1=0

Wy multiply elements

-12x^2+16x*4-1=0

Wy multiply elements

-12x^2+64x-1=0

a = -12; b = 64; c = -1;
Δ = b2-4ac
Δ = 642-4·(-12)·(-1)
Δ = 4048
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:

$\sqrt{\Delta}=\sqrt{4048}=\sqrt{16*253}=\sqrt{16}*\sqrt{253}=4\sqrt{253}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(64)-4\sqrt{253}}{2*-12}=\frac{-64-4\sqrt{253}}{-24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(64)+4\sqrt{253}}{2*-12}=\frac{-64+4\sqrt{253}}{-24}
$