(3x^2+24x+23)/(x+7)=0

Solution for (3x^2+24x+23)/(x+7)=0 equation:

(3x^2+24x+23)/(x+7)=0


Domain of the equation: (x+7)!=0

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

x!=-7

x∈R


We multiply all the terms by the denominator


(3x^2+24x+23)=0

We get rid of parentheses

3x^2+24x+23=0

a = 3; b = 24; c = +23;
Δ = b2-4ac
Δ = 242-4·3·23
Δ = 300
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:

$\sqrt{\Delta}=\sqrt{300}=\sqrt{100*3}=\sqrt{100}*\sqrt{3}=10\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-10\sqrt{3}}{2*3}=\frac{-24-10\sqrt{3}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+10\sqrt{3}}{2*3}=\frac{-24+10\sqrt{3}}{6}
$