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

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

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

We multiply parentheses ..

3(+6x^2+14x-15x-35)=0

We multiply parentheses

18x^2+42x-45x-105=0

We add all the numbers together, and all the variables

18x^2-3x-105=0

a = 18; b = -3; c = -105;
Δ = b2-4ac
Δ = -32-4·18·(-105)
Δ = 7569
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{7569}=87$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-87}{2*18}=\frac{-84}{36}
=-2+1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+87}{2*18}=\frac{90}{36}
=2+1/2
$