(x-7)(4x-1)=0

Solution for (x-7)(4x-1)=0 equation:

(x-7)(4x-1)=0

We multiply parentheses ..

(+4x^2-1x-28x+7)=0

We get rid of parentheses

4x^2-1x-28x+7=0

We add all the numbers together, and all the variables

4x^2-29x+7=0

a = 4; b = -29; c = +7;
Δ = b2-4ac
Δ = -292-4·4·7
Δ = 729
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{729}=27$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-29)-27}{2*4}=\frac{2}{8}
=1/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-29)+27}{2*4}=\frac{56}{8}
=7
$