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

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

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

We multiply parentheses ..

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

We multiply parentheses

28x^2+16x-98x-56=0

We add all the numbers together, and all the variables

28x^2-82x-56=0

a = 28; b = -82; c = -56;
Δ = b2-4ac
Δ = -822-4·28·(-56)
Δ = 12996
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{12996}=114$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-82)-114}{2*28}=\frac{-32}{56}
=-4/7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-82)+114}{2*28}=\frac{196}{56}
=3+1/2
$