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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses ..

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

15x^2+11x-3=0

a = 15; b = 11; c = -3;
Δ = b2-4ac
Δ = 112-4·15·(-3)
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{-(11)-\sqrt{301}}{2*15}=\frac{-11-\sqrt{301}}{30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+\sqrt{301}}{2*15}=\frac{-11+\sqrt{301}}{30}
$