(-8/9)y=-16/7

Solution for (-8/9)y=-16/7 equation:

(-8/9)y=-16/7

We move all terms to the left:

(-8/9)y-(-16/7)=0


Domain of the equation: 9)y!=0

y!=0/1

y!=0

y∈R


We multiply parentheses

-8y^2-(-16/7)=0

We get rid of parentheses

-8y^2+16/7=0

We multiply all the terms by the denominator


-8y^2*7+16=0

Wy multiply elements

-56y^2+16=0

a = -56; b = 0; c = +16;
Δ = b2-4ac
Δ = 02-4·(-56)·16
Δ = 3584
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:

$\sqrt{\Delta}=\sqrt{3584}=\sqrt{256*14}=\sqrt{256}*\sqrt{14}=16\sqrt{14}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-16\sqrt{14}}{2*-56}=\frac{0-16\sqrt{14}}{-112}
=-\frac{16\sqrt{14}}{-112}
=-\frac{\sqrt{14}}{-7}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+16\sqrt{14}}{2*-56}=\frac{0+16\sqrt{14}}{-112}
=\frac{16\sqrt{14}}{-112}
=\frac{\sqrt{14}}{-7}
$