8y+2y+3y=2-10y+3y2

Solution for 8y+2y+3y=2-10y+3y2 equation:

8y+2y+3y=2-10y+3y^2

We move all terms to the left:

8y+2y+3y-(2-10y+3y^2)=0

We add all the numbers together, and all the variables

-(2-10y+3y^2)+13y=0

We get rid of parentheses

-3y^2+10y+13y-2=0

We add all the numbers together, and all the variables

-3y^2+23y-2=0

a = -3; b = 23; c = -2;
Δ = b2-4ac
Δ = 232-4·(-3)·(-2)
Δ = 505
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{-(23)-\sqrt{505}}{2*-3}=\frac{-23-\sqrt{505}}{-6}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(23)+\sqrt{505}}{2*-3}=\frac{-23+\sqrt{505}}{-6}
$