(a^2-11a+30)/(a-6)=0

Solution for (a^2-11a+30)/(a-6)=0 equation:

(a^2-11a+30)/(a-6)=0


Domain of the equation: (a-6)!=0

We move all terms containing a to the left, all other terms to the right

a!=6

a∈R


We multiply all the terms by the denominator


(a^2-11a+30)=0

We get rid of parentheses

a^2-11a+30=0

a = 1; b = -11; c = +30;
Δ = b2-4ac
Δ = -112-4·1·30
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-1}{2*1}=\frac{10}{2}
=5
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+1}{2*1}=\frac{12}{2}
=6
$