Y=-x2+2x+18Y=5x-10

Solution for Y=-x2+2x+18Y=5x-10 equation:

=-Y2+2Y+18=5Y-10

We move all terms to the left:

-(-Y2+2Y+18)=0

We add all the numbers together, and all the variables

-(-1Y^2+2Y+18)=0

We get rid of parentheses

1Y^2-2Y-18=0

We add all the numbers together, and all the variables

Y^2-2Y-18=0

a = 1; b = -2; c = -18;
Δ = b2-4ac
Δ = -22-4·1·(-18)
Δ = 76
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:

$\sqrt{\Delta}=\sqrt{76}=\sqrt{4*19}=\sqrt{4}*\sqrt{19}=2\sqrt{19}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{19}}{2*1}=\frac{2-2\sqrt{19}}{2}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{19}}{2*1}=\frac{2+2\sqrt{19}}{2}
$