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

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

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

We move all terms to the left:

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

We multiply parentheses ..

(+3x^2+15x-2x-10)-1=0

We get rid of parentheses

3x^2+15x-2x-10-1=0

We add all the numbers together, and all the variables

3x^2+13x-11=0

a = 3; b = 13; c = -11;
Δ = b2-4ac
Δ = 132-4·3·(-11)
Δ = 301
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{301}}{2*3}=\frac{-13-\sqrt{301}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+\sqrt{301}}{2*3}=\frac{-13+\sqrt{301}}{6}
$