(5/9)(y+3)=40

Solution for (5/9)(y+3)=40 equation:

(5/9)(y+3)=40

We move all terms to the left:

(5/9)(y+3)-(40)=0


Domain of the equation: 9)(y+3)!=0

y∈R


We add all the numbers together, and all the variables

(+5/9)(y+3)-40=0

We multiply parentheses ..

(+5y^2+5/9*3)-40=0

We multiply all the terms by the denominator


(+5y^2+5-40*9*3)=0

We get rid of parentheses

5y^2+5-40*9*3=0

We add all the numbers together, and all the variables

5y^2-1075=0

a = 5; b = 0; c = -1075;
Δ = b2-4ac
Δ = 02-4·5·(-1075)
Δ = 21500
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:

$\sqrt{\Delta}=\sqrt{21500}=\sqrt{100*215}=\sqrt{100}*\sqrt{215}=10\sqrt{215}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-10\sqrt{215}}{2*5}=\frac{0-10\sqrt{215}}{10}
=-\frac{10\sqrt{215}}{10}
=-\sqrt{215}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+10\sqrt{215}}{2*5}=\frac{0+10\sqrt{215}}{10}
=\frac{10\sqrt{215}}{10}
=\sqrt{215}
$