(2x-3)(3x-2)=10x+13

Solution for (2x-3)(3x-2)=10x+13 equation:

(2x-3)(3x-2)=10x+13

We move all terms to the left:

(2x-3)(3x-2)-(10x+13)=0

We get rid of parentheses

(2x-3)(3x-2)-10x-13=0

We multiply parentheses ..

(+6x^2-4x-9x+6)-10x-13=0

We get rid of parentheses

6x^2-4x-9x-10x+6-13=0

We add all the numbers together, and all the variables

6x^2-23x-7=0

a = 6; b = -23; c = -7;
Δ = b2-4ac
Δ = -232-4·6·(-7)
Δ = 697
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-23)-\sqrt{697}}{2*6}=\frac{23-\sqrt{697}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-23)+\sqrt{697}}{2*6}=\frac{23+\sqrt{697}}{12}
$