(2y+5)(2y+17)=180

Solution for (2y+5)(2y+17)=180 equation:

(2y+5)(2y+17)=180

We move all terms to the left:

(2y+5)(2y+17)-(180)=0

We multiply parentheses ..

(+4y^2+34y+10y+85)-180=0

We get rid of parentheses

4y^2+34y+10y+85-180=0

We add all the numbers together, and all the variables

4y^2+44y-95=0

a = 4; b = 44; c = -95;
Δ = b2-4ac
Δ = 442-4·4·(-95)
Δ = 3456
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:

$\sqrt{\Delta}=\sqrt{3456}=\sqrt{576*6}=\sqrt{576}*\sqrt{6}=24\sqrt{6}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(44)-24\sqrt{6}}{2*4}=\frac{-44-24\sqrt{6}}{8}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(44)+24\sqrt{6}}{2*4}=\frac{-44+24\sqrt{6}}{8}
$