(6x^2+26x+24)/(3x+4)=0

Solution for (6x^2+26x+24)/(3x+4)=0 equation:

(6x^2+26x+24)/(3x+4)=0


Domain of the equation: (3x+4)!=0

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

3x!=-4

x!=-4/3

x!=-1+1/3

x∈R


We multiply all the terms by the denominator


(6x^2+26x+24)=0

We get rid of parentheses

6x^2+26x+24=0

a = 6; b = 26; c = +24;
Δ = b2-4ac
Δ = 262-4·6·24
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{-(26)-10}{2*6}=\frac{-36}{12}
=-3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(26)+10}{2*6}=\frac{-16}{12}
=-1+1/3
$