6x^2=672-24x

Solution for 6x^2=672-24x equation:

6x^2=672-24x

We move all terms to the left:

6x^2-(672-24x)=0

We add all the numbers together, and all the variables

6x^2-(-24x+672)=0

We get rid of parentheses

6x^2+24x-672=0

a = 6; b = 24; c = -672;
Δ = b2-4ac
Δ = 242-4·6·(-672)
Δ = 16704
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:

$\sqrt{\Delta}=\sqrt{16704}=\sqrt{576*29}=\sqrt{576}*\sqrt{29}=24\sqrt{29}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-24\sqrt{29}}{2*6}=\frac{-24-24\sqrt{29}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+24\sqrt{29}}{2*6}=\frac{-24+24\sqrt{29}}{12}
$