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

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

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

We multiply parentheses ..

6(+18x^2+24x-21x-28)=0

We multiply parentheses

108x^2+144x-126x-168=0

We add all the numbers together, and all the variables

108x^2+18x-168=0

a = 108; b = 18; c = -168;
Δ = b2-4ac
Δ = 182-4·108·(-168)
Δ = 72900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{72900}=270$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-270}{2*108}=\frac{-288}{216}
=-1+1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+270}{2*108}=\frac{252}{216}
=1+1/6
$