6x+18=1/4x+12

Solution for 6x+18=1/4x+12 equation:

6x+18=1/4x+12

We move all terms to the left:

6x+18-(1/4x+12)=0


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

x∈R


We get rid of parentheses

6x-1/4x-12+18=0

We multiply all the terms by the denominator


6x*4x-12*4x+18*4x-1=0

Wy multiply elements

24x^2-48x+72x-1=0

We add all the numbers together, and all the variables

24x^2+24x-1=0

a = 24; b = 24; c = -1;
Δ = b2-4ac
Δ = 242-4·24·(-1)
Δ = 672
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:

$\sqrt{\Delta}=\sqrt{672}=\sqrt{16*42}=\sqrt{16}*\sqrt{42}=4\sqrt{42}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-4\sqrt{42}}{2*24}=\frac{-24-4\sqrt{42}}{48}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+4\sqrt{42}}{2*24}=\frac{-24+4\sqrt{42}}{48}
$