0=y^2-10y-47

Solution for 0=y^2-10y-47 equation:

0=y^2-10y-47

We move all terms to the left:

0-(y^2-10y-47)=0

We add all the numbers together, and all the variables

-(y^2-10y-47)=0

We get rid of parentheses

-y^2+10y+47=0

We add all the numbers together, and all the variables

-1y^2+10y+47=0

a = -1; b = 10; c = +47;
Δ = b2-4ac
Δ = 102-4·(-1)·47
Δ = 288
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:

$\sqrt{\Delta}=\sqrt{288}=\sqrt{144*2}=\sqrt{144}*\sqrt{2}=12\sqrt{2}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-12\sqrt{2}}{2*-1}=\frac{-10-12\sqrt{2}}{-2}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+12\sqrt{2}}{2*-1}=\frac{-10+12\sqrt{2}}{-2}
$