6(3-1/4x)=3/4x

Solution for 6(3-1/4x)=3/4x equation:

6(3-1/4x)=3/4x

We move all terms to the left:

6(3-1/4x)-(3/4x)=0


Domain of the equation: 4x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

6(-1/4x+3)-(+3/4x)=0

We multiply parentheses

-6x-(+3/4x)+18=0

We get rid of parentheses

-6x-3/4x+18=0

We multiply all the terms by the denominator


-6x*4x+18*4x-3=0

Wy multiply elements

-24x^2+72x-3=0

a = -24; b = 72; c = -3;
Δ = b2-4ac
Δ = 722-4·(-24)·(-3)
Δ = 4896
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:

$\sqrt{\Delta}=\sqrt{4896}=\sqrt{144*34}=\sqrt{144}*\sqrt{34}=12\sqrt{34}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(72)-12\sqrt{34}}{2*-24}=\frac{-72-12\sqrt{34}}{-48}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(72)+12\sqrt{34}}{2*-24}=\frac{-72+12\sqrt{34}}{-48}
$