Y+3=-4x(x+7)

Solution for Y+3=-4x(x+7) equation:

+3=-4Y(Y+7)

We move all terms to the left:

+3-(-4Y(Y+7))=0


We calculate terms in parentheses: -(-4Y(Y+7)), so:

-4Y(Y+7)

We multiply parentheses

-4Y^2-28Y

Back to the equation:

-(-4Y^2-28Y)


We get rid of parentheses

4Y^2+28Y+3=0

a = 4; b = 28; c = +3;
Δ = b2-4ac
Δ = 282-4·4·3
Δ = 736
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:

$\sqrt{\Delta}=\sqrt{736}=\sqrt{16*46}=\sqrt{16}*\sqrt{46}=4\sqrt{46}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(28)-4\sqrt{46}}{2*4}=\frac{-28-4\sqrt{46}}{8}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(28)+4\sqrt{46}}{2*4}=\frac{-28+4\sqrt{46}}{8}
$