(x-7)(4x-3)=0

Solution for (x-7)(4x-3)=0 equation:

(x-7)(4x-3)=0

We multiply parentheses ..

(+4x^2-3x-28x+21)=0

We get rid of parentheses

4x^2-3x-28x+21=0

We add all the numbers together, and all the variables

4x^2-31x+21=0

a = 4; b = -31; c = +21;
Δ = b2-4ac
Δ = -312-4·4·21
Δ = 625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{625}=25$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-31)-25}{2*4}=\frac{6}{8}
=3/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-31)+25}{2*4}=\frac{56}{8}
=7
$