6x^2+45x-768=56

Solution for 6x^2+45x-768=56 equation:

6x^2+45x-768=56

We move all terms to the left:

6x^2+45x-768-(56)=0

We add all the numbers together, and all the variables

6x^2+45x-824=0

a = 6; b = 45; c = -824;
Δ = b2-4ac
Δ = 452-4·6·(-824)
Δ = 21801
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:

$\sqrt{\Delta}=\sqrt{21801}=\sqrt{169*129}=\sqrt{169}*\sqrt{129}=13\sqrt{129}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(45)-13\sqrt{129}}{2*6}=\frac{-45-13\sqrt{129}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(45)+13\sqrt{129}}{2*6}=\frac{-45+13\sqrt{129}}{12}
$