Y=x^2+4x-150

Solution for Y=x^2+4x-150 equation:

=Y^2+4Y-150

We move all terms to the left:

-(Y^2+4Y-150)=0

We get rid of parentheses

-Y^2-4Y+150=0

We add all the numbers together, and all the variables

-1Y^2-4Y+150=0

a = -1; b = -4; c = +150;
Δ = b2-4ac
Δ = -42-4·(-1)·150
Δ = 616
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:

$\sqrt{\Delta}=\sqrt{616}=\sqrt{4*154}=\sqrt{4}*\sqrt{154}=2\sqrt{154}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-2\sqrt{154}}{2*-1}=\frac{4-2\sqrt{154}}{-2}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+2\sqrt{154}}{2*-1}=\frac{4+2\sqrt{154}}{-2}
$