24=3x^2+24x+7

Solution for 24=3x^2+24x+7 equation:

24=3x^2+24x+7

We move all terms to the left:

24-(3x^2+24x+7)=0

We get rid of parentheses

-3x^2-24x-7+24=0

We add all the numbers together, and all the variables

-3x^2-24x+17=0

a = -3; b = -24; c = +17;
Δ = b2-4ac
Δ = -242-4·(-3)·17
Δ = 780
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:

$\sqrt{\Delta}=\sqrt{780}=\sqrt{4*195}=\sqrt{4}*\sqrt{195}=2\sqrt{195}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-2\sqrt{195}}{2*-3}=\frac{24-2\sqrt{195}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+2\sqrt{195}}{2*-3}=\frac{24+2\sqrt{195}}{-6}
$