(2x-17)(4x+11)=0

Solution for (2x-17)(4x+11)=0 equation:

(2x-17)(4x+11)=0

We multiply parentheses ..

(+8x^2+22x-68x-187)=0

We get rid of parentheses

8x^2+22x-68x-187=0

We add all the numbers together, and all the variables

8x^2-46x-187=0

a = 8; b = -46; c = -187;
Δ = b2-4ac
Δ = -462-4·8·(-187)
Δ = 8100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{8100}=90$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-46)-90}{2*8}=\frac{-44}{16}
=-2+3/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-46)+90}{2*8}=\frac{136}{16}
=8+1/2
$