Y=x^2+18x+10

Solution for Y=x^2+18x+10 equation:

=Y^2+18Y+10

We move all terms to the left:

-(Y^2+18Y+10)=0

We get rid of parentheses

-Y^2-18Y-10=0

We add all the numbers together, and all the variables

-1Y^2-18Y-10=0

a = -1; b = -18; c = -10;
Δ = b2-4ac
Δ = -182-4·(-1)·(-10)
Δ = 284
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:

$\sqrt{\Delta}=\sqrt{284}=\sqrt{4*71}=\sqrt{4}*\sqrt{71}=2\sqrt{71}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-2\sqrt{71}}{2*-1}=\frac{18-2\sqrt{71}}{-2}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+2\sqrt{71}}{2*-1}=\frac{18+2\sqrt{71}}{-2}
$