Y=5x^2+27x-18

Solution for Y=5x^2+27x-18 equation:

=5Y^2+27Y-18

We move all terms to the left:

-(5Y^2+27Y-18)=0

We get rid of parentheses

-5Y^2-27Y+18=0

a = -5; b = -27; c = +18;
Δ = b2-4ac
Δ = -272-4·(-5)·18
Δ = 1089
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1089}=33$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-27)-33}{2*-5}=\frac{-6}{-10}
=3/5
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-27)+33}{2*-5}=\frac{60}{-10}
=-6
$