-3x(x+7)=24

Solution for -3x(x+7)=24 equation:

-3x(x+7)=24

We move all terms to the left:

-3x(x+7)-(24)=0

We multiply parentheses

-3x^2-21x-24=0

a = -3; b = -21; c = -24;
Δ = b2-4ac
Δ = -212-4·(-3)·(-24)
Δ = 153
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:

$\sqrt{\Delta}=\sqrt{153}=\sqrt{9*17}=\sqrt{9}*\sqrt{17}=3\sqrt{17}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-21)-3\sqrt{17}}{2*-3}=\frac{21-3\sqrt{17}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+3\sqrt{17}}{2*-3}=\frac{21+3\sqrt{17}}{-6}
$