6x+4/12x+4=0

Solution for 6x+4/12x+4=0 equation:

6x+4/12x+4=0


Domain of the equation: 12x!=0

x!=0/12

x!=0

x∈R


We multiply all the terms by the denominator


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

Wy multiply elements

72x^2+48x+4=0

a = 72; b = 48; c = +4;
Δ = b2-4ac
Δ = 482-4·72·4
Δ = 1152
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:

$\sqrt{\Delta}=\sqrt{1152}=\sqrt{576*2}=\sqrt{576}*\sqrt{2}=24\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(48)-24\sqrt{2}}{2*72}=\frac{-48-24\sqrt{2}}{144}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(48)+24\sqrt{2}}{2*72}=\frac{-48+24\sqrt{2}}{144}
$