(4x-19)(2x+17)=0

Solution for (4x-19)(2x+17)=0 equation:

(4x-19)(2x+17)=0

We multiply parentheses ..

(+8x^2+68x-38x-323)=0

We get rid of parentheses

8x^2+68x-38x-323=0

We add all the numbers together, and all the variables

8x^2+30x-323=0

a = 8; b = 30; c = -323;
Δ = b2-4ac
Δ = 302-4·8·(-323)
Δ = 11236
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{11236}=106$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-106}{2*8}=\frac{-136}{16}
=-8+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+106}{2*8}=\frac{76}{16}
=4+3/4
$