9y(4y+y)=37

Solution for 9y(4y+y)=37 equation:

9y(4y+y)=37

We move all terms to the left:

9y(4y+y)-(37)=0

We add all the numbers together, and all the variables

9y(+5y)-37=0

We multiply parentheses

45y^2-37=0

a = 45; b = 0; c = -37;
Δ = b2-4ac
Δ = 02-4·45·(-37)
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{-(0)-6\sqrt{185}}{2*45}=\frac{0-6\sqrt{185}}{90}
=-\frac{6\sqrt{185}}{90}
=-\frac{\sqrt{185}}{15}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{185}}{2*45}=\frac{0+6\sqrt{185}}{90}
=\frac{6\sqrt{185}}{90}
=\frac{\sqrt{185}}{15}
$