Y=x^2+14x+42

Solution for Y=x^2+14x+42 equation:

=Y^2+14Y+42

We move all terms to the left:

-(Y^2+14Y+42)=0

We get rid of parentheses

-Y^2-14Y-42=0

We add all the numbers together, and all the variables

-1Y^2-14Y-42=0

a = -1; b = -14; c = -42;
Δ = b2-4ac
Δ = -142-4·(-1)·(-42)
Δ = 28
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:

$\sqrt{\Delta}=\sqrt{28}=\sqrt{4*7}=\sqrt{4}*\sqrt{7}=2\sqrt{7}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-2\sqrt{7}}{2*-1}=\frac{14-2\sqrt{7}}{-2}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+2\sqrt{7}}{2*-1}=\frac{14+2\sqrt{7}}{-2}
$