(-4/3)y=-4/5

Solution for (-4/3)y=-4/5 equation:

(-4/3)y=-4/5

We move all terms to the left:

(-4/3)y-(-4/5)=0


Domain of the equation: 3)y!=0

y!=0/1

y!=0

y∈R


We multiply parentheses

-4y^2-(-4/5)=0

We get rid of parentheses

-4y^2+4/5=0

We multiply all the terms by the denominator


-4y^2*5+4=0

Wy multiply elements

-20y^2+4=0

a = -20; b = 0; c = +4;
Δ = b2-4ac
Δ = 02-4·(-20)·4
Δ = 320
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:

$\sqrt{\Delta}=\sqrt{320}=\sqrt{64*5}=\sqrt{64}*\sqrt{5}=8\sqrt{5}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{5}}{2*-20}=\frac{0-8\sqrt{5}}{-40}
=-\frac{8\sqrt{5}}{-40}
=-\frac{\sqrt{5}}{-5}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{5}}{2*-20}=\frac{0+8\sqrt{5}}{-40}
=\frac{8\sqrt{5}}{-40}
=\frac{\sqrt{5}}{-5}
$