2/3y+(-8)=-12.5y+150

Solution for 2/3y+(-8)=-12.5y+150 equation:

2/3y+(-8)=-12.5y+150

We move all terms to the left:

2/3y+(-8)-(-12.5y+150)=0


Domain of the equation: 3y!=0

y!=0/3

y!=0

y∈R


We add all the numbers together, and all the variables

2/3y-(-12.5y+150)-8=0

We get rid of parentheses

2/3y+12.5y-150-8=0

We multiply all the terms by the denominator


(12.5y)*3y-150*3y-8*3y+2=0

We add all the numbers together, and all the variables

(+12.5y)*3y-150*3y-8*3y+2=0

We multiply parentheses

36y^2-150*3y-8*3y+2=0

Wy multiply elements

36y^2-450y-24y+2=0

We add all the numbers together, and all the variables

36y^2-474y+2=0

a = 36; b = -474; c = +2;
Δ = b2-4ac
Δ = -4742-4·36·2
Δ = 224388
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:

$\sqrt{\Delta}=\sqrt{224388}=\sqrt{36*6233}=\sqrt{36}*\sqrt{6233}=6\sqrt{6233}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-474)-6\sqrt{6233}}{2*36}=\frac{474-6\sqrt{6233}}{72}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-474)+6\sqrt{6233}}{2*36}=\frac{474+6\sqrt{6233}}{72}
$