(3x-13)(2x-3)=0

Solution for (3x-13)(2x-3)=0 equation:

(3x-13)(2x-3)=0

We multiply parentheses ..

(+6x^2-9x-26x+39)=0

We get rid of parentheses

6x^2-9x-26x+39=0

We add all the numbers together, and all the variables

6x^2-35x+39=0

a = 6; b = -35; c = +39;
Δ = b2-4ac
Δ = -352-4·6·39
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-35)-17}{2*6}=\frac{18}{12}
=1+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-35)+17}{2*6}=\frac{52}{12}
=4+1/3
$