5(x-1)(3x+4)=0

Solution for 5(x-1)(3x+4)=0 equation:

5(x-1)(3x+4)=0

We multiply parentheses ..

5(+3x^2+4x-3x-4)=0

We multiply parentheses

15x^2+20x-15x-20=0

We add all the numbers together, and all the variables

15x^2+5x-20=0

a = 15; b = 5; c = -20;
Δ = b2-4ac
Δ = 52-4·15·(-20)
Δ = 1225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1225}=35$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-35}{2*15}=\frac{-40}{30}
=-1+1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+35}{2*15}=\frac{30}{30}
=1
$