9y^2-37y=-36

Solution for 9y^2-37y=-36 equation:

9y^2-37y=-36

We move all terms to the left:

9y^2-37y-(-36)=0

We add all the numbers together, and all the variables

9y^2-37y+36=0

a = 9; b = -37; c = +36;
Δ = b2-4ac
Δ = -372-4·9·36
Δ = 73
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-37)-\sqrt{73}}{2*9}=\frac{37-\sqrt{73}}{18}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-37)+\sqrt{73}}{2*9}=\frac{37+\sqrt{73}}{18}
$