9-14x=3x^2+24

Solution for 9-14x=3x^2+24 equation:

9-14x=3x^2+24

We move all terms to the left:

9-14x-(3x^2+24)=0

We get rid of parentheses

-3x^2-14x-24+9=0

We add all the numbers together, and all the variables

-3x^2-14x-15=0

a = -3; b = -14; c = -15;
Δ = b2-4ac
Δ = -142-4·(-3)·(-15)
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-4}{2*-3}=\frac{10}{-6}
=-1+2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+4}{2*-3}=\frac{18}{-6}
=-3
$