(x-4)(x-3)=72

Solution for (x-4)(x-3)=72 equation:

(x-4)(x-3)=72

We move all terms to the left:

(x-4)(x-3)-(72)=0

We multiply parentheses ..

(+x^2-3x-4x+12)-72=0

We get rid of parentheses

x^2-3x-4x+12-72=0

We add all the numbers together, and all the variables

x^2-7x-60=0

a = 1; b = -7; c = -60;
Δ = b2-4ac
Δ = -72-4·1·(-60)
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-17}{2*1}=\frac{-10}{2}
=-5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+17}{2*1}=\frac{24}{2}
=12
$