(x-7)(7x-2)=0

Solution for (x-7)(7x-2)=0 equation:

(x-7)(7x-2)=0

We multiply parentheses ..

(+7x^2-2x-49x+14)=0

We get rid of parentheses

7x^2-2x-49x+14=0

We add all the numbers together, and all the variables

7x^2-51x+14=0

a = 7; b = -51; c = +14;
Δ = b2-4ac
Δ = -512-4·7·14
Δ = 2209
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2209}=47$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-51)-47}{2*7}=\frac{4}{14}
=2/7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-51)+47}{2*7}=\frac{98}{14}
=7
$