0=y^2-38y-98

Solution for 0=y^2-38y-98 equation:

0=y^2-38y-98

We move all terms to the left:

0-(y^2-38y-98)=0

We add all the numbers together, and all the variables

-(y^2-38y-98)=0

We get rid of parentheses

-y^2+38y+98=0

We add all the numbers together, and all the variables

-1y^2+38y+98=0

a = -1; b = 38; c = +98;
Δ = b2-4ac
Δ = 382-4·(-1)·98
Δ = 1836
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:

$\sqrt{\Delta}=\sqrt{1836}=\sqrt{36*51}=\sqrt{36}*\sqrt{51}=6\sqrt{51}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(38)-6\sqrt{51}}{2*-1}=\frac{-38-6\sqrt{51}}{-2}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(38)+6\sqrt{51}}{2*-1}=\frac{-38+6\sqrt{51}}{-2}
$