x^2+44=-15x

Solution for x^2+44=-15x equation:

x^2+44=-15x

We move all terms to the left:

x^2+44-(-15x)=0

We get rid of parentheses

x^2+15x+44=0

a = 1; b = 15; c = +44;
Δ = b2-4ac
Δ = 152-4·1·44
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-7}{2*1}=\frac{-22}{2}
=-11
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+7}{2*1}=\frac{-8}{2}
=-4
$