(3x-17)(2x+9)=0

Solution for (3x-17)(2x+9)=0 equation:

(3x-17)(2x+9)=0

We multiply parentheses ..

(+6x^2+27x-34x-153)=0

We get rid of parentheses

6x^2+27x-34x-153=0

We add all the numbers together, and all the variables

6x^2-7x-153=0

a = 6; b = -7; c = -153;
Δ = b2-4ac
Δ = -72-4·6·(-153)
Δ = 3721
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3721}=61$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-61}{2*6}=\frac{-54}{12}
=-4+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+61}{2*6}=\frac{68}{12}
=5+2/3
$