X^2+6=54-2x

Solution for X^2+6=54-2x equation:

X^2+6=54-2X

We move all terms to the left:

X^2+6-(54-2X)=0

We add all the numbers together, and all the variables

X^2-(-2X+54)+6=0

We get rid of parentheses

X^2+2X-54+6=0

We add all the numbers together, and all the variables

X^2+2X-48=0

a = 1; b = 2; c = -48;
Δ = b2-4ac
Δ = 22-4·1·(-48)
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-14}{2*1}=\frac{-16}{2}
=-8
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+14}{2*1}=\frac{12}{2}
=6
$