4.3y+8(6-y)y=2

Solution for 4.3y+8(6-y)y=2 equation:

4.3y+8(6-y)y=2

We move all terms to the left:

4.3y+8(6-y)y-(2)=0

We add all the numbers together, and all the variables

4.3y+8(-1y+6)y-2=0

We multiply parentheses

-8y^2+4.3y+48y-2=0

We add all the numbers together, and all the variables

-8y^2+52.3y-2=0

a = -8; b = 52.3; c = -2;
Δ = b2-4ac
Δ = 52.32-4·(-8)·(-2)
Δ = 2671.29
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{-(52.3)-\sqrt{2671.29}}{2*-8}=\frac{-52.3-\sqrt{2671.29}}{-16}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(52.3)+\sqrt{2671.29}}{2*-8}=\frac{-52.3+\sqrt{2671.29}}{-16}
$