Y=5x^2+27x-3

Solution for Y=5x^2+27x-3 equation:

=5Y^2+27Y-3

We move all terms to the left:

-(5Y^2+27Y-3)=0

We get rid of parentheses

-5Y^2-27Y+3=0

a = -5; b = -27; c = +3;
Δ = b2-4ac
Δ = -272-4·(-5)·3
Δ = 789
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{-(-27)-\sqrt{789}}{2*-5}=\frac{27-\sqrt{789}}{-10}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-27)+\sqrt{789}}{2*-5}=\frac{27+\sqrt{789}}{-10}
$