3x+12/6x+24=0

Solution for 3x+12/6x+24=0 equation:

3x+12/6x+24=0


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R


We multiply all the terms by the denominator


3x*6x+24*6x+12=0

Wy multiply elements

18x^2+144x+12=0

a = 18; b = 144; c = +12;
Δ = b2-4ac
Δ = 1442-4·18·12
Δ = 19872
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:

$\sqrt{\Delta}=\sqrt{19872}=\sqrt{144*138}=\sqrt{144}*\sqrt{138}=12\sqrt{138}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(144)-12\sqrt{138}}{2*18}=\frac{-144-12\sqrt{138}}{36}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(144)+12\sqrt{138}}{2*18}=\frac{-144+12\sqrt{138}}{36}
$