5y+8(y-2)y=-1

Solution for 5y+8(y-2)y=-1 equation:

5y+8(y-2)y=-1

We move all terms to the left:

5y+8(y-2)y-(-1)=0

We add all the numbers together, and all the variables

5y+8(y-2)y+1=0

We multiply parentheses

8y^2+5y-16y+1=0

We add all the numbers together, and all the variables

8y^2-11y+1=0

a = 8; b = -11; c = +1;
Δ = b2-4ac
Δ = -112-4·8·1
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{-(-11)-\sqrt{89}}{2*8}=\frac{11-\sqrt{89}}{16}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+\sqrt{89}}{2*8}=\frac{11+\sqrt{89}}{16}
$