11*x*x-54x+63=0

Solution for 11*x*x-54x+63=0 equation:

11x*x-54x+63=0

We add all the numbers together, and all the variables

-54x+11x*x+63=0

Wy multiply elements

11x^2-54x+63=0

a = 11; b = -54; c = +63;
Δ = b2-4ac
Δ = -542-4·11·63
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-54)-12}{2*11}=\frac{42}{22}
=1+10/11
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-54)+12}{2*11}=\frac{66}{22}
=3
$