7x(4x-1)=0

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

7x(4x-1)=0

We multiply parentheses

28x^2-7x=0

a = 28; b = -7; c = 0;
Δ = b2-4ac
Δ = -72-4·28·0
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{-(-7)-7}{2*28}=\frac{0}{56}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+7}{2*28}=\frac{14}{56}
=1/4
$