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

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

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

We move all terms to the left:

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

We multiply parentheses ..

(+15x^2+6x-10x-4)-2=0

We get rid of parentheses

15x^2+6x-10x-4-2=0

We add all the numbers together, and all the variables

15x^2-4x-6=0

a = 15; b = -4; c = -6;
Δ = b2-4ac
Δ = -42-4·15·(-6)
Δ = 376
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{376}=\sqrt{4*94}=\sqrt{4}*\sqrt{94}=2\sqrt{94}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-2\sqrt{94}}{2*15}=\frac{4-2\sqrt{94}}{30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+2\sqrt{94}}{2*15}=\frac{4+2\sqrt{94}}{30}
$