0=10y^2-20y-21

Solution for 0=10y^2-20y-21 equation:

0=10y^2-20y-21

We move all terms to the left:

0-(10y^2-20y-21)=0

We add all the numbers together, and all the variables

-(10y^2-20y-21)=0

We get rid of parentheses

-10y^2+20y+21=0

a = -10; b = 20; c = +21;
Δ = b2-4ac
Δ = 202-4·(-10)·21
Δ = 1240
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:

$\sqrt{\Delta}=\sqrt{1240}=\sqrt{4*310}=\sqrt{4}*\sqrt{310}=2\sqrt{310}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-2\sqrt{310}}{2*-10}=\frac{-20-2\sqrt{310}}{-20}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+2\sqrt{310}}{2*-10}=\frac{-20+2\sqrt{310}}{-20}
$