y-(35/100y)=65

Solution for y-(35/100y)=65 equation:

y-(35/100y)=65

We move all terms to the left:

y-(35/100y)-(65)=0


Domain of the equation: 100y)!=0

y!=0/1

y!=0

y∈R


We add all the numbers together, and all the variables

y-(+35/100y)-65=0

We get rid of parentheses

y-35/100y-65=0

We multiply all the terms by the denominator


y*100y-65*100y-35=0

Wy multiply elements

100y^2-6500y-35=0

a = 100; b = -6500; c = -35;
Δ = b2-4ac
Δ = -65002-4·100·(-35)
Δ = 42264000
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:

$\sqrt{\Delta}=\sqrt{42264000}=\sqrt{14400*2935}=\sqrt{14400}*\sqrt{2935}=120\sqrt{2935}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6500)-120\sqrt{2935}}{2*100}=\frac{6500-120\sqrt{2935}}{200}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6500)+120\sqrt{2935}}{2*100}=\frac{6500+120\sqrt{2935}}{200}
$