(10x-23)(3x+19)=0

Solution for (10x-23)(3x+19)=0 equation:

(10x-23)(3x+19)=0

We multiply parentheses ..

(+30x^2+190x-69x-437)=0

We get rid of parentheses

30x^2+190x-69x-437=0

We add all the numbers together, and all the variables

30x^2+121x-437=0

a = 30; b = 121; c = -437;
Δ = b2-4ac
Δ = 1212-4·30·(-437)
Δ = 67081
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{67081}=259$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(121)-259}{2*30}=\frac{-380}{60}
=-6+1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(121)+259}{2*30}=\frac{138}{60}
=2+3/10
$