Y=180-10x2

Solution for Y=180-10x2 equation:

=180-10Y^2

We move all terms to the left:

-(180-10Y^2)=0

We get rid of parentheses

10Y^2-180=0

a = 10; b = 0; c = -180;
Δ = b2-4ac
Δ = 02-4·10·(-180)
Δ = 7200
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:

$\sqrt{\Delta}=\sqrt{7200}=\sqrt{3600*2}=\sqrt{3600}*\sqrt{2}=60\sqrt{2}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-60\sqrt{2}}{2*10}=\frac{0-60\sqrt{2}}{20}
=-\frac{60\sqrt{2}}{20}
=-3\sqrt{2}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+60\sqrt{2}}{2*10}=\frac{0+60\sqrt{2}}{20}
=\frac{60\sqrt{2}}{20}
=3\sqrt{2}
$