3x^2+7x+14=-7x

Solution for 3x^2+7x+14=-7x equation:

3x^2+7x+14=-7x

We move all terms to the left:

3x^2+7x+14-(-7x)=0

We get rid of parentheses

3x^2+7x+7x+14=0

We add all the numbers together, and all the variables

3x^2+14x+14=0

a = 3; b = 14; c = +14;
Δ = b2-4ac
Δ = 142-4·3·14
Δ = 28
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:

$\sqrt{\Delta}=\sqrt{28}=\sqrt{4*7}=\sqrt{4}*\sqrt{7}=2\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-2\sqrt{7}}{2*3}=\frac{-14-2\sqrt{7}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+2\sqrt{7}}{2*3}=\frac{-14+2\sqrt{7}}{6}
$