Y=x^2-15x+11

Solution for Y=x^2-15x+11 equation:

=Y^2-15Y+11

We move all terms to the left:

-(Y^2-15Y+11)=0

We get rid of parentheses

-Y^2+15Y-11=0

We add all the numbers together, and all the variables

-1Y^2+15Y-11=0

a = -1; b = 15; c = -11;
Δ = b2-4ac
Δ = 152-4·(-1)·(-11)
Δ = 181
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-\sqrt{181}}{2*-1}=\frac{-15-\sqrt{181}}{-2}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+\sqrt{181}}{2*-1}=\frac{-15+\sqrt{181}}{-2}
$