(3a-2)(-3-5a)=1

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

(3a-2)(-3-5a)=1

We move all terms to the left:

(3a-2)(-3-5a)-(1)=0

We add all the numbers together, and all the variables

(3a-2)(-5a-3)-1=0

We multiply parentheses ..

(-15a^2-9a+10a+6)-1=0

We get rid of parentheses

-15a^2-9a+10a+6-1=0

We add all the numbers together, and all the variables

-15a^2+a+5=0

a = -15; b = 1; c = +5;
Δ = b2-4ac
Δ = 12-4·(-15)·5
Δ = 301
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-\sqrt{301}}{2*-15}=\frac{-1-\sqrt{301}}{-30}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{301}}{2*-15}=\frac{-1+\sqrt{301}}{-30}
$