96/8y=35y

Solution for 96/8y=35y equation:

96/8y=35y

We move all terms to the left:

96/8y-(35y)=0


Domain of the equation: 8y!=0

y!=0/8

y!=0

y∈R


We add all the numbers together, and all the variables

-35y+96/8y=0

We multiply all the terms by the denominator


-35y*8y+96=0

Wy multiply elements

-280y^2+96=0

a = -280; b = 0; c = +96;
Δ = b2-4ac
Δ = 02-4·(-280)·96
Δ = 107520
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:

$\sqrt{\Delta}=\sqrt{107520}=\sqrt{1024*105}=\sqrt{1024}*\sqrt{105}=32\sqrt{105}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-32\sqrt{105}}{2*-280}=\frac{0-32\sqrt{105}}{-560}
=-\frac{32\sqrt{105}}{-560}
=-\frac{2\sqrt{105}}{-35}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+32\sqrt{105}}{2*-280}=\frac{0+32\sqrt{105}}{-560}
=\frac{32\sqrt{105}}{-560}
=\frac{2\sqrt{105}}{-35}
$