(2x+3)(3x-5)=-14

Solution for (2x+3)(3x-5)=-14 equation:

(2x+3)(3x-5)=-14

We move all terms to the left:

(2x+3)(3x-5)-(-14)=0

We add all the numbers together, and all the variables

(2x+3)(3x-5)+14=0

We multiply parentheses ..

(+6x^2-10x+9x-15)+14=0

We get rid of parentheses

6x^2-10x+9x-15+14=0

We add all the numbers together, and all the variables

6x^2-1x-1=0

a = 6; b = -1; c = -1;
Δ = b2-4ac
Δ = -12-4·6·(-1)
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-5}{2*6}=\frac{-4}{12}
=-1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+5}{2*6}=\frac{6}{12}
=1/2
$