4y^2+9y+21=180

Solution for 4y^2+9y+21=180 equation:

4y^2+9y+21=180

We move all terms to the left:

4y^2+9y+21-(180)=0

We add all the numbers together, and all the variables

4y^2+9y-159=0

a = 4; b = 9; c = -159;
Δ = b2-4ac
Δ = 92-4·4·(-159)
Δ = 2625
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:

$\sqrt{\Delta}=\sqrt{2625}=\sqrt{25*105}=\sqrt{25}*\sqrt{105}=5\sqrt{105}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-5\sqrt{105}}{2*4}=\frac{-9-5\sqrt{105}}{8}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+5\sqrt{105}}{2*4}=\frac{-9+5\sqrt{105}}{8}
$