(2+1/3)y-5=16

Solution for (2+1/3)y-5=16 equation:

(2+1/3)y-5=16

We move all terms to the left:

(2+1/3)y-5-(16)=0


Domain of the equation: 3)y!=0

y!=0/1

y!=0

y∈R


We add all the numbers together, and all the variables

(1/3+2)y-5-16=0

We add all the numbers together, and all the variables

(1/3+2)y-21=0

We multiply parentheses

y^2+2y-21=0

a = 1; b = 2; c = -21;
Δ = b2-4ac
Δ = 22-4·1·(-21)
Δ = 88
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:

$\sqrt{\Delta}=\sqrt{88}=\sqrt{4*22}=\sqrt{4}*\sqrt{22}=2\sqrt{22}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{22}}{2*1}=\frac{-2-2\sqrt{22}}{2}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{22}}{2*1}=\frac{-2+2\sqrt{22}}{2}
$