2/3y+y-4=34

Solution for 2/3y+y-4=34 equation:

2/3y+y-4=34

We move all terms to the left:

2/3y+y-4-(34)=0


Domain of the equation: 3y!=0

y!=0/3

y!=0

y∈R


We add all the numbers together, and all the variables

y+2/3y-38=0

We multiply all the terms by the denominator


y*3y-38*3y+2=0

Wy multiply elements

3y^2-114y+2=0

a = 3; b = -114; c = +2;
Δ = b2-4ac
Δ = -1142-4·3·2
Δ = 12972
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:

$\sqrt{\Delta}=\sqrt{12972}=\sqrt{4*3243}=\sqrt{4}*\sqrt{3243}=2\sqrt{3243}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-114)-2\sqrt{3243}}{2*3}=\frac{114-2\sqrt{3243}}{6}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-114)+2\sqrt{3243}}{2*3}=\frac{114+2\sqrt{3243}}{6}
$