3x(x+3)=4

Solution for 3x(x+3)=4 equation:

3x(x+3)=4

We move all terms to the left:

3x(x+3)-(4)=0

We multiply parentheses

3x^2+9x-4=0

a = 3; b = 9; c = -4;
Δ = b2-4ac
Δ = 92-4·3·(-4)
Δ = 129
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-\sqrt{129}}{2*3}=\frac{-9-\sqrt{129}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+\sqrt{129}}{2*3}=\frac{-9+\sqrt{129}}{6}
$