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

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

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

We multiply parentheses ..

(+28x^2-8x-49x+14)=0

We get rid of parentheses

28x^2-8x-49x+14=0

We add all the numbers together, and all the variables

28x^2-57x+14=0

a = 28; b = -57; c = +14;
Δ = b2-4ac
Δ = -572-4·28·14
Δ = 1681
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1681}=41$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-57)-41}{2*28}=\frac{16}{56}
=2/7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-57)+41}{2*28}=\frac{98}{56}
=1+3/4
$