(8x-11)(2x+19)=0

Solution for (8x-11)(2x+19)=0 equation:

(8x-11)(2x+19)=0

We multiply parentheses ..

(+16x^2+152x-22x-209)=0

We get rid of parentheses

16x^2+152x-22x-209=0

We add all the numbers together, and all the variables

16x^2+130x-209=0

a = 16; b = 130; c = -209;
Δ = b2-4ac
Δ = 1302-4·16·(-209)
Δ = 30276
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{30276}=174$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(130)-174}{2*16}=\frac{-304}{32}
=-9+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(130)+174}{2*16}=\frac{44}{32}
=1+3/8
$