y-9/10y=25

Solution for y-9/10y=25 equation:

y-9/10y=25

We move all terms to the left:

y-9/10y-(25)=0


Domain of the equation: 10y!=0

y!=0/10

y!=0

y∈R


We multiply all the terms by the denominator


y*10y-25*10y-9=0

Wy multiply elements

10y^2-250y-9=0

a = 10; b = -250; c = -9;
Δ = b2-4ac
Δ = -2502-4·10·(-9)
Δ = 62860
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:

$\sqrt{\Delta}=\sqrt{62860}=\sqrt{4*15715}=\sqrt{4}*\sqrt{15715}=2\sqrt{15715}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-250)-2\sqrt{15715}}{2*10}=\frac{250-2\sqrt{15715}}{20}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-250)+2\sqrt{15715}}{2*10}=\frac{250+2\sqrt{15715}}{20}
$