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

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

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

We multiply parentheses ..

5(+3x^2-5x+18x-30)=0

We multiply parentheses

15x^2-25x+90x-150=0

We add all the numbers together, and all the variables

15x^2+65x-150=0

a = 15; b = 65; c = -150;
Δ = b2-4ac
Δ = 652-4·15·(-150)
Δ = 13225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{13225}=115$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(65)-115}{2*15}=\frac{-180}{30}
=-6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(65)+115}{2*15}=\frac{50}{30}
=1+2/3
$