(x-7)(4x-2)=0

Solution for (x-7)(4x-2)=0 equation:

(x-7)(4x-2)=0

We multiply parentheses ..

(+4x^2-2x-28x+14)=0

We get rid of parentheses

4x^2-2x-28x+14=0

We add all the numbers together, and all the variables

4x^2-30x+14=0

a = 4; b = -30; c = +14;
Δ = b2-4ac
Δ = -302-4·4·14
Δ = 676
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{676}=26$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-26}{2*4}=\frac{4}{8}
=1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+26}{2*4}=\frac{56}{8}
=7
$