(11x+17)(2x-13)=0

Solution for (11x+17)(2x-13)=0 equation:

(11x+17)(2x-13)=0

We multiply parentheses ..

(+22x^2-143x+34x-221)=0

We get rid of parentheses

22x^2-143x+34x-221=0

We add all the numbers together, and all the variables

22x^2-109x-221=0

a = 22; b = -109; c = -221;
Δ = b2-4ac
Δ = -1092-4·22·(-221)
Δ = 31329
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{31329}=177$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-109)-177}{2*22}=\frac{-68}{44}
=-1+6/11
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-109)+177}{2*22}=\frac{286}{44}
=6+1/2
$