Y=x^2-2x-19/5

Solution for Y=x^2-2x-19/5 equation:

=Y^2-2Y-19/5

We move all terms to the left:

-(Y^2-2Y-19/5)=0

We get rid of parentheses

-Y^2+2Y+19/5=0

We multiply all the terms by the denominator


-Y^2*5+2Y*5+19=0

Wy multiply elements

-5Y^2+10Y+19=0

a = -5; b = 10; c = +19;
Δ = b2-4ac
Δ = 102-4·(-5)·19
Δ = 480
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:

$\sqrt{\Delta}=\sqrt{480}=\sqrt{16*30}=\sqrt{16}*\sqrt{30}=4\sqrt{30}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-4\sqrt{30}}{2*-5}=\frac{-10-4\sqrt{30}}{-10}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+4\sqrt{30}}{2*-5}=\frac{-10+4\sqrt{30}}{-10}
$