(1/6(12x)-18)=2x-3

Solution for (1/6(12x)-18)=2x-3 equation:

(1/6(12x)-18)=2x-3

We move all terms to the left:

(1/6(12x)-18)-(2x-3)=0


Domain of the equation: 612x-18)!=0

x∈R


We get rid of parentheses

1/612x-2x-18+3=0

We multiply all the terms by the denominator


-2x*612x-18*612x+3*612x+1=0

Wy multiply elements

-1224x^2-11016x+1836x+1=0

We add all the numbers together, and all the variables

-1224x^2-9180x+1=0

a = -1224; b = -9180; c = +1;
Δ = b2-4ac
Δ = -91802-4·(-1224)·1
Δ = 84277296
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:

$\sqrt{\Delta}=\sqrt{84277296}=\sqrt{144*585259}=\sqrt{144}*\sqrt{585259}=12\sqrt{585259}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9180)-12\sqrt{585259}}{2*-1224}=\frac{9180-12\sqrt{585259}}{-2448}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9180)+12\sqrt{585259}}{2*-1224}=\frac{9180+12\sqrt{585259}}{-2448}
$