(2x+5)(3x-1)=9

Solution for (2x+5)(3x-1)=9 equation:

(2x+5)(3x-1)=9

We move all terms to the left:

(2x+5)(3x-1)-(9)=0

We multiply parentheses ..

(+6x^2-2x+15x-5)-9=0

We get rid of parentheses

6x^2-2x+15x-5-9=0

We add all the numbers together, and all the variables

6x^2+13x-14=0

a = 6; b = 13; c = -14;
Δ = b2-4ac
Δ = 132-4·6·(-14)
Δ = 505
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{-(13)-\sqrt{505}}{2*6}=\frac{-13-\sqrt{505}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+\sqrt{505}}{2*6}=\frac{-13+\sqrt{505}}{12}
$