Y=-400+130x+-10x^2

Solution for Y=-400+130x+-10x^2 equation:

=-400+130Y+-10Y^2

We move all terms to the left:

-(-400+130Y+-10Y^2)=0

We use the square of the difference formula

-(-400+130Y-10Y^2)=0

We get rid of parentheses

10Y^2-130Y+400=0

a = 10; b = -130; c = +400;
Δ = b2-4ac
Δ = -1302-4·10·400
Δ = 900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{900}=30$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-130)-30}{2*10}=\frac{100}{20}
=5
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-130)+30}{2*10}=\frac{160}{20}
=8
$