6x(4x-7)=0

Solution for 6x(4x-7)=0 equation:

6x(4x-7)=0

We multiply parentheses

24x^2-42x=0

a = 24; b = -42; c = 0;
Δ = b2-4ac
Δ = -422-4·24·0
Δ = 1764
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1764}=42$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-42)-42}{2*24}=\frac{0}{48}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-42)+42}{2*24}=\frac{84}{48}
=1+3/4
$