(3x+7)(2x-3)=13

Solution for (3x+7)(2x-3)=13 equation:

(3x+7)(2x-3)=13

We move all terms to the left:

(3x+7)(2x-3)-(13)=0

We multiply parentheses ..

(+6x^2-9x+14x-21)-13=0

We get rid of parentheses

6x^2-9x+14x-21-13=0

We add all the numbers together, and all the variables

6x^2+5x-34=0

a = 6; b = 5; c = -34;
Δ = b2-4ac
Δ = 52-4·6·(-34)
Δ = 841
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{841}=29$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-29}{2*6}=\frac{-34}{12}
=-2+5/6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+29}{2*6}=\frac{24}{12}
=2
$