(8x-5)(3x-19)=0

Solution for (8x-5)(3x-19)=0 equation:

(8x-5)(3x-19)=0

We multiply parentheses ..

(+24x^2-152x-15x+95)=0

We get rid of parentheses

24x^2-152x-15x+95=0

We add all the numbers together, and all the variables

24x^2-167x+95=0

a = 24; b = -167; c = +95;
Δ = b2-4ac
Δ = -1672-4·24·95
Δ = 18769
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{18769}=137$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-167)-137}{2*24}=\frac{30}{48}
=5/8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-167)+137}{2*24}=\frac{304}{48}
=6+1/3
$