5(y-2)7y=-32

Solution for 5(y-2)7y=-32 equation:

5(y-2)7y=-32

We move all terms to the left:

5(y-2)7y-(-32)=0

We add all the numbers together, and all the variables

5(y-2)7y+32=0

We multiply parentheses

35y^2-70y+32=0

a = 35; b = -70; c = +32;
Δ = b2-4ac
Δ = -702-4·35·32
Δ = 420
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{420}=\sqrt{4*105}=\sqrt{4}*\sqrt{105}=2\sqrt{105}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-70)-2\sqrt{105}}{2*35}=\frac{70-2\sqrt{105}}{70}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-70)+2\sqrt{105}}{2*35}=\frac{70+2\sqrt{105}}{70}
$