(4/7)y=6/5

Solution for (4/7)y=6/5 equation:

(4/7)y=6/5

We move all terms to the left:

(4/7)y-(6/5)=0


Domain of the equation: 7)y!=0

y!=0/1

y!=0

y∈R


We add all the numbers together, and all the variables

(+4/7)y-(+6/5)=0

We multiply parentheses

4y^2-(+6/5)=0

We get rid of parentheses

4y^2-6/5=0

We multiply all the terms by the denominator


4y^2*5-6=0

Wy multiply elements

20y^2-6=0

a = 20; b = 0; c = -6;
Δ = b2-4ac
Δ = 02-4·20·(-6)
Δ = 480
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:

$\sqrt{\Delta}=\sqrt{480}=\sqrt{16*30}=\sqrt{16}*\sqrt{30}=4\sqrt{30}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{30}}{2*20}=\frac{0-4\sqrt{30}}{40}
=-\frac{4\sqrt{30}}{40}
=-\frac{\sqrt{30}}{10}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{30}}{2*20}=\frac{0+4\sqrt{30}}{40}
=\frac{4\sqrt{30}}{40}
=\frac{\sqrt{30}}{10}
$