-19x^2-27x+120=48

Solution for -19x^2-27x+120=48 equation:

-19x^2-27x+120=48

We move all terms to the left:

-19x^2-27x+120-(48)=0

We add all the numbers together, and all the variables

-19x^2-27x+72=0

a = -19; b = -27; c = +72;
Δ = b2-4ac
Δ = -272-4·(-19)·72
Δ = 6201
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:

$\sqrt{\Delta}=\sqrt{6201}=\sqrt{9*689}=\sqrt{9}*\sqrt{689}=3\sqrt{689}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-27)-3\sqrt{689}}{2*-19}=\frac{27-3\sqrt{689}}{-38}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-27)+3\sqrt{689}}{2*-19}=\frac{27+3\sqrt{689}}{-38}
$