1/5y+9.y=15

Solution for 1/5y+9.y=15 equation:

1/5y+9.y=15

We move all terms to the left:

1/5y+9.y-(15)=0


Domain of the equation: 5y!=0

y!=0/5

y!=0

y∈R


We add all the numbers together, and all the variables

9.y+1/5y-15=0

We multiply all the terms by the denominator


(9.y)*5y-15*5y+1=0

We add all the numbers together, and all the variables

(+9.y)*5y-15*5y+1=0

We multiply parentheses

45y^2-15*5y+1=0

Wy multiply elements

45y^2-75y+1=0

a = 45; b = -75; c = +1;
Δ = b2-4ac
Δ = -752-4·45·1
Δ = 5445
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:

$\sqrt{\Delta}=\sqrt{5445}=\sqrt{1089*5}=\sqrt{1089}*\sqrt{5}=33\sqrt{5}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-75)-33\sqrt{5}}{2*45}=\frac{75-33\sqrt{5}}{90}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-75)+33\sqrt{5}}{2*45}=\frac{75+33\sqrt{5}}{90}
$