3(2x-5)(x+7)=0

Solution for 3(2x-5)(x+7)=0 equation:

3(2x-5)(x+7)=0

We multiply parentheses ..

3(+2x^2+14x-5x-35)=0

We multiply parentheses

6x^2+42x-15x-105=0

We add all the numbers together, and all the variables

6x^2+27x-105=0

a = 6; b = 27; c = -105;
Δ = b2-4ac
Δ = 272-4·6·(-105)
Δ = 3249
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3249}=57$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(27)-57}{2*6}=\frac{-84}{12}
=-7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(27)+57}{2*6}=\frac{30}{12}
=2+1/2
$