3x^2=-14-23x

Solution for 3x^2=-14-23x equation:

3x^2=-14-23x

We move all terms to the left:

3x^2-(-14-23x)=0

We add all the numbers together, and all the variables

3x^2-(-23x-14)=0

We get rid of parentheses

3x^2+23x+14=0

a = 3; b = 23; c = +14;
Δ = b2-4ac
Δ = 232-4·3·14
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(23)-19}{2*3}=\frac{-42}{6}
=-7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(23)+19}{2*3}=\frac{-4}{6}
=-2/3
$