(3x-8)(5x+1)=0

Solution for (3x-8)(5x+1)=0 equation:

(3x-8)(5x+1)=0

We multiply parentheses ..

(+15x^2+3x-40x-8)=0

We get rid of parentheses

15x^2+3x-40x-8=0

We add all the numbers together, and all the variables

15x^2-37x-8=0

a = 15; b = -37; c = -8;
Δ = b2-4ac
Δ = -372-4·15·(-8)
Δ = 1849
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1849}=43$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-37)-43}{2*15}=\frac{-6}{30}
=-1/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-37)+43}{2*15}=\frac{80}{30}
=2+2/3
$