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{-42}{12}
=-3+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+51}{2*6}=\frac{60}{12}
=5
$