(x-4)(x+18)=4

Solution for (x-4)(x+18)=4 equation:

(x-4)(x+18)=4

We move all terms to the left:

(x-4)(x+18)-(4)=0

We multiply parentheses ..

(+x^2+18x-4x-72)-4=0

We get rid of parentheses

x^2+18x-4x-72-4=0

We add all the numbers together, and all the variables

x^2+14x-76=0

a = 1; b = 14; c = -76;
Δ = b2-4ac
Δ = 142-4·1·(-76)
Δ = 500
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{500}=\sqrt{100*5}=\sqrt{100}*\sqrt{5}=10\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-10\sqrt{5}}{2*1}=\frac{-14-10\sqrt{5}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+10\sqrt{5}}{2*1}=\frac{-14+10\sqrt{5}}{2}
$