3x+5/3x+6=0

Solution for 3x+5/3x+6=0 equation:

3x+5/3x+6=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We multiply all the terms by the denominator


3x*3x+6*3x+5=0

Wy multiply elements

9x^2+18x+5=0

a = 9; b = 18; c = +5;
Δ = b2-4ac
Δ = 182-4·9·5
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-12}{2*9}=\frac{-30}{18}
=-1+2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+12}{2*9}=\frac{-6}{18}
=-1/3
$