4(y+5)2y-7y=-1

Solution for 4(y+5)2y-7y=-1 equation:

4(y+5)2y-7y=-1

We move all terms to the left:

4(y+5)2y-7y-(-1)=0

We add all the numbers together, and all the variables

-7y+4(y+5)2y+1=0

We multiply parentheses

8y^2-7y+40y+1=0

We add all the numbers together, and all the variables

8y^2+33y+1=0

a = 8; b = 33; c = +1;
Δ = b2-4ac
Δ = 332-4·8·1
Δ = 1057
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{-(33)-\sqrt{1057}}{2*8}=\frac{-33-\sqrt{1057}}{16}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(33)+\sqrt{1057}}{2*8}=\frac{-33+\sqrt{1057}}{16}
$