5(2x-6)(3x+1)=0

Solution for 5(2x-6)(3x+1)=0 equation:

5(2x-6)(3x+1)=0

We multiply parentheses ..

5(+6x^2+2x-18x-6)=0

We multiply parentheses

30x^2+10x-90x-30=0

We add all the numbers together, and all the variables

30x^2-80x-30=0

a = 30; b = -80; c = -30;
Δ = b2-4ac
Δ = -802-4·30·(-30)
Δ = 10000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{10000}=100$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-80)-100}{2*30}=\frac{-20}{60}
=-1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-80)+100}{2*30}=\frac{180}{60}
=3
$