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

Solution for 6(x-5)(x+3)=0 equation:

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

We multiply parentheses ..

6(+x^2+3x-5x-15)=0

We multiply parentheses

6x^2+18x-30x-90=0

We add all the numbers together, and all the variables

6x^2-12x-90=0

a = 6; b = -12; c = -90;
Δ = b2-4ac
Δ = -122-4·6·(-90)
Δ = 2304
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2304}=48$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-48}{2*6}=\frac{-36}{12}
=-3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+48}{2*6}=\frac{60}{12}
=5
$