18y^2+9y=45

Solution for 18y^2+9y=45 equation:

18y^2+9y=45

We move all terms to the left:

18y^2+9y-(45)=0

a = 18; b = 9; c = -45;
Δ = b2-4ac
Δ = 92-4·18·(-45)
Δ = 3321
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:

$\sqrt{\Delta}=\sqrt{3321}=\sqrt{81*41}=\sqrt{81}*\sqrt{41}=9\sqrt{41}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-9\sqrt{41}}{2*18}=\frac{-9-9\sqrt{41}}{36}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+9\sqrt{41}}{2*18}=\frac{-9+9\sqrt{41}}{36}
$