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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses ..

(+6x^2+9x-2x-3)+5=0

We get rid of parentheses

6x^2+9x-2x-3+5=0

We add all the numbers together, and all the variables

6x^2+7x+2=0

a = 6; b = 7; c = +2;
Δ = b2-4ac
Δ = 72-4·6·2
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-1}{2*6}=\frac{-8}{12}
=-2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+1}{2*6}=\frac{-6}{12}
=-1/2
$