4/5y+5(1/5y-6)=9/5y-30

Solution for 4/5y+5(1/5y-6)=9/5y-30 equation:

4/5y+5(1/5y-6)=9/5y-30

We move all terms to the left:

4/5y+5(1/5y-6)-(9/5y-30)=0


Domain of the equation: 5y!=0

y!=0/5

y!=0

y∈R



Domain of the equation: 5y-6)!=0

y∈R



Domain of the equation: 5y-30)!=0

y∈R


We multiply parentheses

4/5y+5y-(9/5y-30)-30=0

We get rid of parentheses

4/5y+5y-9/5y+30-30=0

We multiply all the terms by the denominator


5y*5y+30*5y-30*5y+4-9=0

We add all the numbers together, and all the variables

5y*5y+30*5y-30*5y-5=0

Wy multiply elements

25y^2+150y-150y-5=0

We add all the numbers together, and all the variables

25y^2-5=0

a = 25; b = 0; c = -5;
Δ = b2-4ac
Δ = 02-4·25·(-5)
Δ = 500
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:

$\sqrt{\Delta}=\sqrt{500}=\sqrt{100*5}=\sqrt{100}*\sqrt{5}=10\sqrt{5}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-10\sqrt{5}}{2*25}=\frac{0-10\sqrt{5}}{50}
=-\frac{10\sqrt{5}}{50}
=-\frac{\sqrt{5}}{5}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+10\sqrt{5}}{2*25}=\frac{0+10\sqrt{5}}{50}
=\frac{10\sqrt{5}}{50}
=\frac{\sqrt{5}}{5}
$