Y-34=x(x-19)

Solution for Y-34=x(x-19) equation:

-34=Y(Y-19)

We move all terms to the left:

-34-(Y(Y-19))=0


We calculate terms in parentheses: -(Y(Y-19)), so:

Y(Y-19)

We multiply parentheses

Y^2-19Y

Back to the equation:

-(Y^2-19Y)


We get rid of parentheses

-Y^2+19Y-34=0

We add all the numbers together, and all the variables

-1Y^2+19Y-34=0

a = -1; b = 19; c = -34;
Δ = b2-4ac
Δ = 192-4·(-1)·(-34)
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(19)-15}{2*-1}=\frac{-34}{-2}
=+17
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(19)+15}{2*-1}=\frac{-4}{-2}
=+2
$