14x+12=-4x^2

Solution for 14x+12=-4x^2 equation:

14x+12=-4x^2

We move all terms to the left:

14x+12-(-4x^2)=0

We get rid of parentheses

4x^2+14x+12=0

a = 4; b = 14; c = +12;
Δ = b2-4ac
Δ = 142-4·4·12
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{-(14)-2}{2*4}=\frac{-16}{8}
=-2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+2}{2*4}=\frac{-12}{8}
=-1+1/2
$