(3x-17)(7x+11)=0

Solution for (3x-17)(7x+11)=0 equation:

(3x-17)(7x+11)=0

We multiply parentheses ..

(+21x^2+33x-119x-187)=0

We get rid of parentheses

21x^2+33x-119x-187=0

We add all the numbers together, and all the variables

21x^2-86x-187=0

a = 21; b = -86; c = -187;
Δ = b2-4ac
Δ = -862-4·21·(-187)
Δ = 23104
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{23104}=152$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-86)-152}{2*21}=\frac{-66}{42}
=-1+4/7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-86)+152}{2*21}=\frac{238}{42}
=5+2/3
$