3x^2-60x+243=-54

Solution for 3x^2-60x+243=-54 equation:

3x^2-60x+243=-54

We move all terms to the left:

3x^2-60x+243-(-54)=0

We add all the numbers together, and all the variables

3x^2-60x+297=0

a = 3; b = -60; c = +297;
Δ = b2-4ac
Δ = -602-4·3·297
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-60)-6}{2*3}=\frac{54}{6}
=9
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-60)+6}{2*3}=\frac{66}{6}
=11
$