(D^2+6D+10)y=50

Solution for (D^2+6D+10)y=50 equation:

(^2+6+10)D=50

We move all terms to the left:

(^2+6+10)D-(50)=0

We multiply parentheses

D^2+6D+10D-50=0

We add all the numbers together, and all the variables

D^2+16D-50=0

a = 1; b = 16; c = -50;
Δ = b2-4ac
Δ = 162-4·1·(-50)
Δ = 456
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$D_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$D_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{456}=\sqrt{4*114}=\sqrt{4}*\sqrt{114}=2\sqrt{114}$
$D_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-2\sqrt{114}}{2*1}=\frac{-16-2\sqrt{114}}{2}
$
$D_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+2\sqrt{114}}{2*1}=\frac{-16+2\sqrt{114}}{2}
$