(x-4)(x-10)=14

Solution for (x-4)(x-10)=14 equation:

(x-4)(x-10)=14

We move all terms to the left:

(x-4)(x-10)-(14)=0

We multiply parentheses ..

(+x^2-10x-4x+40)-14=0

We get rid of parentheses

x^2-10x-4x+40-14=0

We add all the numbers together, and all the variables

x^2-14x+26=0

a = 1; b = -14; c = +26;
Δ = b2-4ac
Δ = -142-4·1·26
Δ = 92
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:

$\sqrt{\Delta}=\sqrt{92}=\sqrt{4*23}=\sqrt{4}*\sqrt{23}=2\sqrt{23}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-2\sqrt{23}}{2*1}=\frac{14-2\sqrt{23}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+2\sqrt{23}}{2*1}=\frac{14+2\sqrt{23}}{2}
$