y-9/10y=6

Solution for y-9/10y=6 equation:

y-9/10y=6

We move all terms to the left:

y-9/10y-(6)=0


Domain of the equation: 10y!=0

y!=0/10

y!=0

y∈R


We multiply all the terms by the denominator


y*10y-6*10y-9=0

Wy multiply elements

10y^2-60y-9=0

a = 10; b = -60; c = -9;
Δ = b2-4ac
Δ = -602-4·10·(-9)
Δ = 3960
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:

$\sqrt{\Delta}=\sqrt{3960}=\sqrt{36*110}=\sqrt{36}*\sqrt{110}=6\sqrt{110}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-60)-6\sqrt{110}}{2*10}=\frac{60-6\sqrt{110}}{20}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-60)+6\sqrt{110}}{2*10}=\frac{60+6\sqrt{110}}{20}
$