(x-6)(2x-14)=0

Solution for (x-6)(2x-14)=0 equation:

(x-6)(2x-14)=0

We multiply parentheses ..

(+2x^2-14x-12x+84)=0

We get rid of parentheses

2x^2-14x-12x+84=0

We add all the numbers together, and all the variables

2x^2-26x+84=0

a = 2; b = -26; c = +84;
Δ = b2-4ac
Δ = -262-4·2·84
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-26)-2}{2*2}=\frac{24}{4}
=6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-26)+2}{2*2}=\frac{28}{4}
=7
$