6(2x-3)(4x+7)=0

Solution for 6(2x-3)(4x+7)=0 equation:

6(2x-3)(4x+7)=0

We multiply parentheses ..

6(+8x^2+14x-12x-21)=0

We multiply parentheses

48x^2+84x-72x-126=0

We add all the numbers together, and all the variables

48x^2+12x-126=0

a = 48; b = 12; c = -126;
Δ = b2-4ac
Δ = 122-4·48·(-126)
Δ = 24336
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{24336}=156$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-156}{2*48}=\frac{-168}{96}
=-1+3/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+156}{2*48}=\frac{144}{96}
=1+1/2
$