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

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

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

We multiply parentheses ..

3(+2x^2-7x+10x-35)=0

We multiply parentheses

6x^2-21x+30x-105=0

We add all the numbers together, and all the variables

6x^2+9x-105=0

a = 6; b = 9; c = -105;
Δ = b2-4ac
Δ = 92-4·6·(-105)
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{-(9)-51}{2*6}=\frac{-60}{12}
=-5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+51}{2*6}=\frac{42}{12}
=3+1/2
$