(x-10)(x-4)=55

Solution for (x-10)(x-4)=55 equation:

(x-10)(x-4)=55

We move all terms to the left:

(x-10)(x-4)-(55)=0

We multiply parentheses ..

(+x^2-4x-10x+40)-55=0

We get rid of parentheses

x^2-4x-10x+40-55=0

We add all the numbers together, and all the variables

x^2-14x-15=0

a = 1; b = -14; c = -15;
Δ = b2-4ac
Δ = -142-4·1·(-15)
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-16}{2*1}=\frac{-2}{2}
=-1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+16}{2*1}=\frac{30}{2}
=15
$