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

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

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

We move all terms to the left:

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

We multiply parentheses ..

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

6x^2-45x+39=0

a = 6; b = -45; c = +39;
Δ = b2-4ac
Δ = -452-4·6·39
Δ = 1089
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1089}=33$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-45)-33}{2*6}=\frac{12}{12}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-45)+33}{2*6}=\frac{78}{12}
=6+1/2
$