Y=-18x^2+203x+6

Solution for Y=-18x^2+203x+6 equation:

=-18Y^2+203Y+6

We move all terms to the left:

-(-18Y^2+203Y+6)=0

We get rid of parentheses

18Y^2-203Y-6=0

a = 18; b = -203; c = -6;
Δ = b2-4ac
Δ = -2032-4·18·(-6)
Δ = 41641
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{-(-203)-\sqrt{41641}}{2*18}=\frac{203-\sqrt{41641}}{36}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-203)+\sqrt{41641}}{2*18}=\frac{203+\sqrt{41641}}{36}
$