(15x-2)(5x+3)=5

Solution for (15x-2)(5x+3)=5 equation:

(15x-2)(5x+3)=5

We move all terms to the left:

(15x-2)(5x+3)-(5)=0

We multiply parentheses ..

(+75x^2+45x-10x-6)-5=0

We get rid of parentheses

75x^2+45x-10x-6-5=0

We add all the numbers together, and all the variables

75x^2+35x-11=0

a = 75; b = 35; c = -11;
Δ = b2-4ac
Δ = 352-4·75·(-11)
Δ = 4525
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:

$\sqrt{\Delta}=\sqrt{4525}=\sqrt{25*181}=\sqrt{25}*\sqrt{181}=5\sqrt{181}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(35)-5\sqrt{181}}{2*75}=\frac{-35-5\sqrt{181}}{150}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(35)+5\sqrt{181}}{2*75}=\frac{-35+5\sqrt{181}}{150}
$