X(3x+4)=-1

Solution for X(3x+4)=-1 equation:

X(3X+4)=-1

We move all terms to the left:

X(3X+4)-(-1)=0

We add all the numbers together, and all the variables

X(3X+4)+1=0

We multiply parentheses

3X^2+4X+1=0

a = 3; b = 4; c = +1;
Δ = b2-4ac
Δ = 42-4·3·1
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-2}{2*3}=\frac{-6}{6}
=-1
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+2}{2*3}=\frac{-2}{6}
=-1/3
$