(a^2-3a+7)/(a-1)=5

Solution for (a^2-3a+7)/(a-1)=5 equation:

(a^2-3a+7)/(a-1)=5

We move all terms to the left:

(a^2-3a+7)/(a-1)-(5)=0


Domain of the equation: (a-1)!=0

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

a!=1

a∈R


We multiply all the terms by the denominator


(a^2-3a+7)-5*(a-1)=0

We multiply parentheses

(a^2-3a+7)-5a+5=0

We get rid of parentheses

a^2-3a-5a+7+5=0

We add all the numbers together, and all the variables

a^2-8a+12=0

a = 1; b = -8; c = +12;
Δ = b2-4ac
Δ = -82-4·1·12
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-4}{2*1}=\frac{4}{2}
=2
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+4}{2*1}=\frac{12}{2}
=6
$