0=y^2-10y-9

Solution for 0=y^2-10y-9 equation:

0=y^2-10y-9

We move all terms to the left:

0-(y^2-10y-9)=0

We add all the numbers together, and all the variables

-(y^2-10y-9)=0

We get rid of parentheses

-y^2+10y+9=0

We add all the numbers together, and all the variables

-1y^2+10y+9=0

a = -1; b = 10; c = +9;
Δ = b2-4ac
Δ = 102-4·(-1)·9
Δ = 136
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:

$\sqrt{\Delta}=\sqrt{136}=\sqrt{4*34}=\sqrt{4}*\sqrt{34}=2\sqrt{34}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{34}}{2*-1}=\frac{-10-2\sqrt{34}}{-2}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{34}}{2*-1}=\frac{-10+2\sqrt{34}}{-2}
$