-3x^2+42x-147=-48

Solution for -3x^2+42x-147=-48 equation:

-3x^2+42x-147=-48

We move all terms to the left:

-3x^2+42x-147-(-48)=0

We add all the numbers together, and all the variables

-3x^2+42x-99=0

a = -3; b = 42; c = -99;
Δ = b2-4ac
Δ = 422-4·(-3)·(-99)
Δ = 576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{576}=24$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(42)-24}{2*-3}=\frac{-66}{-6}
=+11
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(42)+24}{2*-3}=\frac{-18}{-6}
=+3
$