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

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

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

We add all the numbers together, and all the variables

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

We multiply parentheses ..

(-6x^2-34x+9x+51)=0

We get rid of parentheses

-6x^2-34x+9x+51=0

We add all the numbers together, and all the variables

-6x^2-25x+51=0

a = -6; b = -25; c = +51;
Δ = b2-4ac
Δ = -252-4·(-6)·51
Δ = 1849
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1849}=43$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-25)-43}{2*-6}=\frac{-18}{-12}
=1+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-25)+43}{2*-6}=\frac{68}{-12}
=-5+2/3
$