(X-7)(x-9)=48

Solution for (X-7)(x-9)=48 equation:

(X-7)(X-9)=48

We move all terms to the left:

(X-7)(X-9)-(48)=0

We multiply parentheses ..

(+X^2-9X-7X+63)-48=0

We get rid of parentheses

X^2-9X-7X+63-48=0

We add all the numbers together, and all the variables

X^2-16X+15=0

a = 1; b = -16; c = +15;
Δ = b2-4ac
Δ = -162-4·1·15
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{-(-16)-14}{2*1}=\frac{2}{2}
=1
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+14}{2*1}=\frac{30}{2}
=15
$