(4y-5)(2y+5)=180

Solution for (4y-5)(2y+5)=180 equation:

(4y-5)(2y+5)=180

We move all terms to the left:

(4y-5)(2y+5)-(180)=0

We multiply parentheses ..

(+8y^2+20y-10y-25)-180=0

We get rid of parentheses

8y^2+20y-10y-25-180=0

We add all the numbers together, and all the variables

8y^2+10y-205=0

a = 8; b = 10; c = -205;
Δ = b2-4ac
Δ = 102-4·8·(-205)
Δ = 6660
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:

$\sqrt{\Delta}=\sqrt{6660}=\sqrt{36*185}=\sqrt{36}*\sqrt{185}=6\sqrt{185}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-6\sqrt{185}}{2*8}=\frac{-10-6\sqrt{185}}{16}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+6\sqrt{185}}{2*8}=\frac{-10+6\sqrt{185}}{16}
$