x^2+4x=-4/3

Solution for x^2+4x=-4/3 equation:

x^2+4x=-4/3

We move all terms to the left:

x^2+4x-(-4/3)=0

We get rid of parentheses

x^2+4x+4/3=0

We multiply all the terms by the denominator


x^2*3+4x*3+4=0

Wy multiply elements

3x^2+12x+4=0

a = 3; b = 12; c = +4;
Δ = b2-4ac
Δ = 122-4·3·4
Δ = 96
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:

$\sqrt{\Delta}=\sqrt{96}=\sqrt{16*6}=\sqrt{16}*\sqrt{6}=4\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-4\sqrt{6}}{2*3}=\frac{-12-4\sqrt{6}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+4\sqrt{6}}{2*3}=\frac{-12+4\sqrt{6}}{6}
$