4/5y+y=30

Solution for 4/5y+y=30 equation:

4/5y+y=30

We move all terms to the left:

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


Domain of the equation: 5y!=0

y!=0/5

y!=0

y∈R


We add all the numbers together, and all the variables

y+4/5y-30=0

We multiply all the terms by the denominator


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

Wy multiply elements

5y^2-150y+4=0

a = 5; b = -150; c = +4;
Δ = b2-4ac
Δ = -1502-4·5·4
Δ = 22420
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:

$\sqrt{\Delta}=\sqrt{22420}=\sqrt{4*5605}=\sqrt{4}*\sqrt{5605}=2\sqrt{5605}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-150)-2\sqrt{5605}}{2*5}=\frac{150-2\sqrt{5605}}{10}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-150)+2\sqrt{5605}}{2*5}=\frac{150+2\sqrt{5605}}{10}
$