y2+22y=-43

Solution for y2+22y=-43 equation:

y2+22y=-43

We move all terms to the left:

y2+22y-(-43)=0

We add all the numbers together, and all the variables

y^2+22y+43=0

a = 1; b = 22; c = +43;
Δ = b2-4ac
Δ = 222-4·1·43
Δ = 312
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:

$\sqrt{\Delta}=\sqrt{312}=\sqrt{4*78}=\sqrt{4}*\sqrt{78}=2\sqrt{78}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(22)-2\sqrt{78}}{2*1}=\frac{-22-2\sqrt{78}}{2}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(22)+2\sqrt{78}}{2*1}=\frac{-22+2\sqrt{78}}{2}
$