(6y+8)(7y-12)=180

Solution for (6y+8)(7y-12)=180 equation:

(6y+8)(7y-12)=180

We move all terms to the left:

(6y+8)(7y-12)-(180)=0

We multiply parentheses ..

(+42y^2-72y+56y-96)-180=0

We get rid of parentheses

42y^2-72y+56y-96-180=0

We add all the numbers together, and all the variables

42y^2-16y-276=0

a = 42; b = -16; c = -276;
Δ = b2-4ac
Δ = -162-4·42·(-276)
Δ = 46624
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:

$\sqrt{\Delta}=\sqrt{46624}=\sqrt{16*2914}=\sqrt{16}*\sqrt{2914}=4\sqrt{2914}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-4\sqrt{2914}}{2*42}=\frac{16-4\sqrt{2914}}{84}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+4\sqrt{2914}}{2*42}=\frac{16+4\sqrt{2914}}{84}
$