6(0.25x-2)=9/6x-12

Solution for 6(0.25x-2)=9/6x-12 equation:

6(0.25x-2)=9/6x-12

We move all terms to the left:

6(0.25x-2)-(9/6x-12)=0


Domain of the equation: 6x-12)!=0

x∈R


We multiply parentheses

0x-(9/6x-12)-12=0

We get rid of parentheses

0x-9/6x+12-12=0

We multiply all the terms by the denominator


0x*6x+12*6x-12*6x-9=0

Wy multiply elements

0x^2+72x-72x-9=0

We add all the numbers together, and all the variables

x^2-9=0

a = 1; b = 0; c = -9;
Δ = b2-4ac
Δ = 02-4·1·(-9)
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6}{2*1}=\frac{-6}{2}
=-3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6}{2*1}=\frac{6}{2}
=3
$