-5-(15y-1)(7y-16)-y=2

Solution for -5-(15y-1)(7y-16)-y=2 equation:

-5-(15y-1)(7y-16)-y=2

We move all terms to the left:

-5-(15y-1)(7y-16)-y-(2)=0

We add all the numbers together, and all the variables

-1y-(15y-1)(7y-16)-7=0

We multiply parentheses ..

-(+105y^2-240y-7y+16)-1y-7=0

We get rid of parentheses

-105y^2+240y+7y-1y-16-7=0

We add all the numbers together, and all the variables

-105y^2+246y-23=0

a = -105; b = 246; c = -23;
Δ = b2-4ac
Δ = 2462-4·(-105)·(-23)
Δ = 50856
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{50856}=\sqrt{4*12714}=\sqrt{4}*\sqrt{12714}=2\sqrt{12714}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(246)-2\sqrt{12714}}{2*-105}=\frac{-246-2\sqrt{12714}}{-210}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(246)+2\sqrt{12714}}{2*-105}=\frac{-246+2\sqrt{12714}}{-210}
$