y(5+4y)-2y=35

Solution for y(5+4y)-2y=35 equation:

y(5+4y)-2y=35

We move all terms to the left:

y(5+4y)-2y-(35)=0

We add all the numbers together, and all the variables

y(4y+5)-2y-35=0

We add all the numbers together, and all the variables

-2y+y(4y+5)-35=0

We multiply parentheses

4y^2-2y+5y-35=0

We add all the numbers together, and all the variables

4y^2+3y-35=0

a = 4; b = 3; c = -35;
Δ = b2-4ac
Δ = 32-4·4·(-35)
Δ = 569
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{-(3)-\sqrt{569}}{2*4}=\frac{-3-\sqrt{569}}{8}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{569}}{2*4}=\frac{-3+\sqrt{569}}{8}
$