Y=4.7+0.05x-0.0001x^2

Solution for Y=4.7+0.05x-0.0001x^2 equation:

=4.7+0.05Y-0.0001Y^2

We move all terms to the left:

-(4.7+0.05Y-0.0001Y^2)=0

We get rid of parentheses

0.0001Y^2-0.05Y-4.7=0

a = 0.0001; b = -0.05; c = -4.7;
Δ = b2-4ac
Δ = -0.052-4·0.0001·(-4.7)
Δ = 0.00438
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{-(-0.05)-\sqrt{0.00438}}{2*0.0001}=\frac{0.05-\sqrt{0.00438}}{0.0002}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-0.05)+\sqrt{0.00438}}{2*0.0001}=\frac{0.05+\sqrt{0.00438}}{0.0002}
$