y^2+3y=84

Solution for y^2+3y=84 equation:

y^2+3y=84

We move all terms to the left:

y^2+3y-(84)=0

a = 1; b = 3; c = -84;
Δ = b2-4ac
Δ = 32-4·1·(-84)
Δ = 345
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{-(3)-\sqrt{345}}{2*1}=\frac{-3-\sqrt{345}}{2}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{345}}{2*1}=\frac{-3+\sqrt{345}}{2}
$