10y+y^2=200

Solution for 10y+y^2=200 equation:

10y+y^2=200

We move all terms to the left:

10y+y^2-(200)=0

a = 1; b = 10; c = -200;
Δ = b2-4ac
Δ = 102-4·1·(-200)
Δ = 900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{900}=30$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-30}{2*1}=\frac{-40}{2}
=-20
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+30}{2*1}=\frac{20}{2}
=10
$