(6y-10)(6y+10)=180

Solution for (6y-10)(6y+10)=180 equation:

(6y-10)(6y+10)=180

We move all terms to the left:

(6y-10)(6y+10)-(180)=0

We use the square of the difference formula

36y^2-100-180=0

We add all the numbers together, and all the variables

36y^2-280=0

a = 36; b = 0; c = -280;
Δ = b2-4ac
Δ = 02-4·36·(-280)
Δ = 40320
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:

$\sqrt{\Delta}=\sqrt{40320}=\sqrt{576*70}=\sqrt{576}*\sqrt{70}=24\sqrt{70}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-24\sqrt{70}}{2*36}=\frac{0-24\sqrt{70}}{72}
=-\frac{24\sqrt{70}}{72}
=-\frac{\sqrt{70}}{3}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+24\sqrt{70}}{2*36}=\frac{0+24\sqrt{70}}{72}
=\frac{24\sqrt{70}}{72}
=\frac{\sqrt{70}}{3}
$