13/4x-12=6x

Solution for 13/4x-12=6x equation:

13/4x-12=6x

We move all terms to the left:

13/4x-12-(6x)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We add all the numbers together, and all the variables

-6x+13/4x-12=0

We multiply all the terms by the denominator


-6x*4x-12*4x+13=0

Wy multiply elements

-24x^2-48x+13=0

a = -24; b = -48; c = +13;
Δ = b2-4ac
Δ = -482-4·(-24)·13
Δ = 3552
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:

$\sqrt{\Delta}=\sqrt{3552}=\sqrt{16*222}=\sqrt{16}*\sqrt{222}=4\sqrt{222}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-48)-4\sqrt{222}}{2*-24}=\frac{48-4\sqrt{222}}{-48}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-48)+4\sqrt{222}}{2*-24}=\frac{48+4\sqrt{222}}{-48}
$