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

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

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

We multiply parentheses ..

3(+3x^2+5x-12x-20)=0

We multiply parentheses

9x^2+15x-36x-60=0

We add all the numbers together, and all the variables

9x^2-21x-60=0

a = 9; b = -21; c = -60;
Δ = b2-4ac
Δ = -212-4·9·(-60)
Δ = 2601
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2601}=51$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-21)-51}{2*9}=\frac{-30}{18}
=-1+2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+51}{2*9}=\frac{72}{18}
=4
$