Y=4x^2-5x-10

Solution for Y=4x^2-5x-10 equation:

=4Y^2-5Y-10

We move all terms to the left:

-(4Y^2-5Y-10)=0

We get rid of parentheses

-4Y^2+5Y+10=0

a = -4; b = 5; c = +10;
Δ = b2-4ac
Δ = 52-4·(-4)·10
Δ = 185
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{-(5)-\sqrt{185}}{2*-4}=\frac{-5-\sqrt{185}}{-8}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{185}}{2*-4}=\frac{-5+\sqrt{185}}{-8}
$