(3y+53)(7y-55)=180

Solution for (3y+53)(7y-55)=180 equation:

(3y+53)(7y-55)=180

We move all terms to the left:

(3y+53)(7y-55)-(180)=0

We multiply parentheses ..

(+21y^2-165y+371y-2915)-180=0

We get rid of parentheses

21y^2-165y+371y-2915-180=0

We add all the numbers together, and all the variables

21y^2+206y-3095=0

a = 21; b = 206; c = -3095;
Δ = b2-4ac
Δ = 2062-4·21·(-3095)
Δ = 302416
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:

$\sqrt{\Delta}=\sqrt{302416}=\sqrt{16*18901}=\sqrt{16}*\sqrt{18901}=4\sqrt{18901}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(206)-4\sqrt{18901}}{2*21}=\frac{-206-4\sqrt{18901}}{42}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(206)+4\sqrt{18901}}{2*21}=\frac{-206+4\sqrt{18901}}{42}
$