5y-2y-y^2=y^2-2y-10

Solution for 5y-2y-y^2=y^2-2y-10 equation:

5y-2y-y^2=y^2-2y-10

We move all terms to the left:

5y-2y-y^2-(y^2-2y-10)=0

We add all the numbers together, and all the variables

-1y^2+3y-(y^2-2y-10)=0

We get rid of parentheses

-1y^2-y^2+3y+2y+10=0

We add all the numbers together, and all the variables

-2y^2+5y+10=0

a = -2; b = 5; c = +10;
Δ = b2-4ac
Δ = 52-4·(-2)·10
Δ = 105
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{105}}{2*-2}=\frac{-5-\sqrt{105}}{-4}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{105}}{2*-2}=\frac{-5+\sqrt{105}}{-4}
$