x(x-14)+7(x-14)=0

Solution for x(x-14)+7(x-14)=0 equation:

x(x-14)+7(x-14)=0

We multiply parentheses

x^2-14x+7x-98=0

We add all the numbers together, and all the variables

x^2-7x-98=0

a = 1; b = -7; c = -98;
Δ = b2-4ac
Δ = -72-4·1·(-98)
Δ = 441
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{441}=21$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-21}{2*1}=\frac{-14}{2}
=-7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+21}{2*1}=\frac{28}{2}
=14
$