6(3x-4)(5x+4)=0

Solution for 6(3x-4)(5x+4)=0 equation:

6(3x-4)(5x+4)=0

We multiply parentheses ..

6(+15x^2+12x-20x-16)=0

We multiply parentheses

90x^2+72x-120x-96=0

We add all the numbers together, and all the variables

90x^2-48x-96=0

a = 90; b = -48; c = -96;
Δ = b2-4ac
Δ = -482-4·90·(-96)
Δ = 36864
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36864}=192$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-48)-192}{2*90}=\frac{-144}{180}
=-4/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-48)+192}{2*90}=\frac{240}{180}
=1+1/3
$