Y=4x^2-18x-10

Solution for Y=4x^2-18x-10 equation:

=4Y^2-18Y-10

We move all terms to the left:

-(4Y^2-18Y-10)=0

We get rid of parentheses

-4Y^2+18Y+10=0

a = -4; b = 18; c = +10;
Δ = b2-4ac
Δ = 182-4·(-4)·10
Δ = 484
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{484}=22$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-22}{2*-4}=\frac{-40}{-8}
=+5
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+22}{2*-4}=\frac{4}{-8}
=-1/2
$