y=-2X2-12X-10

Solution for y=-2X2-12X-10 equation:

y=-2y^2-12y-10

We move all terms to the left:

y-(-2y^2-12y-10)=0

We get rid of parentheses

2y^2+12y+y+10=0

We add all the numbers together, and all the variables

2y^2+13y+10=0

a = 2; b = 13; c = +10;
Δ = b2-4ac
Δ = 132-4·2·10
Δ = 89
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{-(13)-\sqrt{89}}{2*2}=\frac{-13-\sqrt{89}}{4}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+\sqrt{89}}{2*2}=\frac{-13+\sqrt{89}}{4}
$