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

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

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

We multiply parentheses ..

(+15x^2+3x-20x-4)=0

We get rid of parentheses

15x^2+3x-20x-4=0

We add all the numbers together, and all the variables

15x^2-17x-4=0

a = 15; b = -17; c = -4;
Δ = b2-4ac
Δ = -172-4·15·(-4)
Δ = 529
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{529}=23$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-17)-23}{2*15}=\frac{-6}{30}
=-1/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-17)+23}{2*15}=\frac{40}{30}
=1+1/3
$