-4y^2+2y-6y+24=0

Solution for -4y^2+2y-6y+24=0 equation:

-4y^2+2y-6y+24=0

We add all the numbers together, and all the variables

-4y^2-4y+24=0

a = -4; b = -4; c = +24;
Δ = b2-4ac
Δ = -42-4·(-4)·24
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-20}{2*-4}=\frac{-16}{-8}
=+2
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+20}{2*-4}=\frac{24}{-8}
=-3
$