(-4/11)y=-16/33

Solution for (-4/11)y=-16/33 equation:

(-4/11)y=-16/33

We move all terms to the left:

(-4/11)y-(-16/33)=0


Domain of the equation: 11)y!=0

y!=0/1

y!=0

y∈R


We multiply parentheses

-4y^2-(-16/33)=0

We get rid of parentheses

-4y^2+16/33=0

We multiply all the terms by the denominator


-4y^2*33+16=0

Wy multiply elements

-132y^2+16=0

a = -132; b = 0; c = +16;
Δ = b2-4ac
Δ = 02-4·(-132)·16
Δ = 8448
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:

$\sqrt{\Delta}=\sqrt{8448}=\sqrt{256*33}=\sqrt{256}*\sqrt{33}=16\sqrt{33}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-16\sqrt{33}}{2*-132}=\frac{0-16\sqrt{33}}{-264}
=-\frac{16\sqrt{33}}{-264}
=-\frac{2\sqrt{33}}{-33}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+16\sqrt{33}}{2*-132}=\frac{0+16\sqrt{33}}{-264}
=\frac{16\sqrt{33}}{-264}
=\frac{2\sqrt{33}}{-33}
$