(3x^2+14x+8)/(3x+2)=0

Solution for (3x^2+14x+8)/(3x+2)=0 equation:

(3x^2+14x+8)/(3x+2)=0


Domain of the equation: (3x+2)!=0

We move all terms containing x to the left, all other terms to the right

3x!=-2

x!=-2/3

x!=-2/3

x∈R


We multiply all the terms by the denominator


(3x^2+14x+8)=0

We get rid of parentheses

3x^2+14x+8=0

a = 3; b = 14; c = +8;
Δ = b2-4ac
Δ = 142-4·3·8
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-10}{2*3}=\frac{-24}{6}
=-4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+10}{2*3}=\frac{-4}{6}
=-2/3
$