20/9*y=10

Solution for 20/9*y=10 equation:

20/9*y=10

We move all terms to the left:

20/9*y-(10)=0


Domain of the equation: 9*y!=0

y!=0/1

y!=0

y∈R


We multiply all the terms by the denominator


-10*9*y+20=0

Wy multiply elements

-90y*y+20=0

Wy multiply elements

-90y^2+20=0

a = -90; b = 0; c = +20;
Δ = b2-4ac
Δ = 02-4·(-90)·20
Δ = 7200
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:

$\sqrt{\Delta}=\sqrt{7200}=\sqrt{3600*2}=\sqrt{3600}*\sqrt{2}=60\sqrt{2}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-60\sqrt{2}}{2*-90}=\frac{0-60\sqrt{2}}{-180}
=-\frac{60\sqrt{2}}{-180}
=-\frac{\sqrt{2}}{-3}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+60\sqrt{2}}{2*-90}=\frac{0+60\sqrt{2}}{-180}
=\frac{60\sqrt{2}}{-180}
=\frac{\sqrt{2}}{-3}
$