(a-1)(a-3)=35

Solution for (a-1)(a-3)=35 equation:

(a-1)(a-3)=35

We move all terms to the left:

(a-1)(a-3)-(35)=0

We multiply parentheses ..

(+a^2-3a-1a+3)-35=0

We get rid of parentheses

a^2-3a-1a+3-35=0

We add all the numbers together, and all the variables

a^2-4a-32=0

a = 1; b = -4; c = -32;
Δ = b2-4ac
Δ = -42-4·1·(-32)
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-12}{2*1}=\frac{-8}{2}
=-4
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+12}{2*1}=\frac{16}{2}
=8
$