3x+4/9x+6=0

Solution for 3x+4/9x+6=0 equation:

3x+4/9x+6=0


Domain of the equation: 9x!=0

x!=0/9

x!=0

x∈R


We multiply all the terms by the denominator


3x*9x+6*9x+4=0

Wy multiply elements

27x^2+54x+4=0

a = 27; b = 54; c = +4;
Δ = b2-4ac
Δ = 542-4·27·4
Δ = 2484
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:

$\sqrt{\Delta}=\sqrt{2484}=\sqrt{36*69}=\sqrt{36}*\sqrt{69}=6\sqrt{69}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(54)-6\sqrt{69}}{2*27}=\frac{-54-6\sqrt{69}}{54}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(54)+6\sqrt{69}}{2*27}=\frac{-54+6\sqrt{69}}{54}
$