13x+4=-3x^2

Solution for 13x+4=-3x^2 equation:

13x+4=-3x^2

We move all terms to the left:

13x+4-(-3x^2)=0

We get rid of parentheses

3x^2+13x+4=0

a = 3; b = 13; c = +4;
Δ = b2-4ac
Δ = 132-4·3·4
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(13)-11}{2*3}=\frac{-24}{6}
=-4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+11}{2*3}=\frac{-2}{6}
=-1/3
$