10^2=y(y+21)

Solution for 10^2=y(y+21) equation:

10^2=y(y+21)

We move all terms to the left:

10^2-(y(y+21))=0

We add all the numbers together, and all the variables

-(y(y+21))+100=0


We calculate terms in parentheses: -(y(y+21)), so:

y(y+21)

We multiply parentheses

y^2+21y

Back to the equation:

-(y^2+21y)


We get rid of parentheses

-y^2-21y+100=0

We add all the numbers together, and all the variables

-1y^2-21y+100=0

a = -1; b = -21; c = +100;
Δ = b2-4ac
Δ = -212-4·(-1)·100
Δ = 841
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{841}=29$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-21)-29}{2*-1}=\frac{-8}{-2}
=+4
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+29}{2*-1}=\frac{50}{-2}
=-25
$