6x^2+24x=56

Solution for 6x^2+24x=56 equation:

6x^2+24x=56

We move all terms to the left:

6x^2+24x-(56)=0

a = 6; b = 24; c = -56;
Δ = b2-4ac
Δ = 242-4·6·(-56)
Δ = 1920
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:

$\sqrt{\Delta}=\sqrt{1920}=\sqrt{64*30}=\sqrt{64}*\sqrt{30}=8\sqrt{30}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-8\sqrt{30}}{2*6}=\frac{-24-8\sqrt{30}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+8\sqrt{30}}{2*6}=\frac{-24+8\sqrt{30}}{12}
$