(x-4)(2x-1)/7=0

Solution for (x-4)(2x-1)/7=0 equation:

(x-4)(2x-1)/7=0

We multiply parentheses ..

(+2x^2-1x-8x+4)/7=0

We multiply all the terms by the denominator


(+2x^2-1x-8x+4)=0

We get rid of parentheses

2x^2-1x-8x+4=0

We add all the numbers together, and all the variables

2x^2-9x+4=0

a = 2; b = -9; c = +4;
Δ = b2-4ac
Δ = -92-4·2·4
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-7}{2*2}=\frac{2}{4}
=1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+7}{2*2}=\frac{16}{4}
=4
$