y^2+3y=45

Solution for y^2+3y=45 equation:

y^2+3y=45

We move all terms to the left:

y^2+3y-(45)=0

a = 1; b = 3; c = -45;
Δ = b2-4ac
Δ = 32-4·1·(-45)
Δ = 189
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:

$\sqrt{\Delta}=\sqrt{189}=\sqrt{9*21}=\sqrt{9}*\sqrt{21}=3\sqrt{21}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-3\sqrt{21}}{2*1}=\frac{-3-3\sqrt{21}}{2}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+3\sqrt{21}}{2*1}=\frac{-3+3\sqrt{21}}{2}
$