6a2-54=(a-3)

Solution for 6a2-54=(a-3) equation:

6a^2-54=(a-3)

We move all terms to the left:

6a^2-54-((a-3))=0


We calculate terms in parentheses: -((a-3)), so:

(a-3)

We get rid of parentheses

a-3

Back to the equation:

-(a-3)


We get rid of parentheses

6a^2-a+3-54=0

We add all the numbers together, and all the variables

6a^2-1a-51=0

a = 6; b = -1; c = -51;
Δ = b2-4ac
Δ = -12-4·6·(-51)
Δ = 1225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1225}=35$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-35}{2*6}=\frac{-34}{12}
=-2+5/6
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+35}{2*6}=\frac{36}{12}
=3
$