4x+12/6x+18=0

Solution for 4x+12/6x+18=0 equation:

4x+12/6x+18=0


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R


We multiply all the terms by the denominator


4x*6x+18*6x+12=0

Wy multiply elements

24x^2+108x+12=0

a = 24; b = 108; c = +12;
Δ = b2-4ac
Δ = 1082-4·24·12
Δ = 10512
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:

$\sqrt{\Delta}=\sqrt{10512}=\sqrt{144*73}=\sqrt{144}*\sqrt{73}=12\sqrt{73}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(108)-12\sqrt{73}}{2*24}=\frac{-108-12\sqrt{73}}{48}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(108)+12\sqrt{73}}{2*24}=\frac{-108+12\sqrt{73}}{48}
$