(x-5)(x)=(14)(6)

Solution for (x-5)(x)=(14)(6) equation:

(x-5)(x)=(14)(6)

We move all terms to the left:

(x-5)(x)-((14)(6))=0

determiningTheFunctionDomain
(x-5)x-146=0

We multiply parentheses

x^2-5x-146=0

a = 1; b = -5; c = -146;
Δ = b2-4ac
Δ = -52-4·1·(-146)
Δ = 609
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{-(-5)-\sqrt{609}}{2*1}=\frac{5-\sqrt{609}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{609}}{2*1}=\frac{5+\sqrt{609}}{2}
$