y+5=2/3y+13

Solution for y+5=2/3y+13 equation:

y+5=2/3y+13

We move all terms to the left:

y+5-(2/3y+13)=0


Domain of the equation: 3y+13)!=0

y∈R


We get rid of parentheses

y-2/3y-13+5=0

We multiply all the terms by the denominator


y*3y-13*3y+5*3y-2=0

Wy multiply elements

3y^2-39y+15y-2=0

We add all the numbers together, and all the variables

3y^2-24y-2=0

a = 3; b = -24; c = -2;
Δ = b2-4ac
Δ = -242-4·3·(-2)
Δ = 600
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:

$\sqrt{\Delta}=\sqrt{600}=\sqrt{100*6}=\sqrt{100}*\sqrt{6}=10\sqrt{6}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-10\sqrt{6}}{2*3}=\frac{24-10\sqrt{6}}{6}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+10\sqrt{6}}{2*3}=\frac{24+10\sqrt{6}}{6}
$