(x-7)(x-2)=(5)(4)

Solution for (x-7)(x-2)=(5)(4) equation:

(x-7)(x-2)=(5)(4)

We move all terms to the left:

(x-7)(x-2)-((5)(4))=0

determiningTheFunctionDomain
(x-7)(x-2)-54=0

We multiply parentheses ..

(+x^2-2x-7x+14)-54=0

We get rid of parentheses

x^2-2x-7x+14-54=0

We add all the numbers together, and all the variables

x^2-9x-40=0

a = 1; b = -9; c = -40;
Δ = b2-4ac
Δ = -92-4·1·(-40)
Δ = 241
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-\sqrt{241}}{2*1}=\frac{9-\sqrt{241}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+\sqrt{241}}{2*1}=\frac{9+\sqrt{241}}{2}
$