(3x-2)(5x-19)=0

Solution for (3x-2)(5x-19)=0 equation:

(3x-2)(5x-19)=0

We multiply parentheses ..

(+15x^2-57x-10x+38)=0

We get rid of parentheses

15x^2-57x-10x+38=0

We add all the numbers together, and all the variables

15x^2-67x+38=0

a = 15; b = -67; c = +38;
Δ = b2-4ac
Δ = -672-4·15·38
Δ = 2209
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2209}=47$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-67)-47}{2*15}=\frac{20}{30}
=2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-67)+47}{2*15}=\frac{114}{30}
=3+4/5
$