2/3y-16-5y=-12

Solution for 2/3y-16-5y=-12 equation:

2/3y-16-5y=-12

We move all terms to the left:

2/3y-16-5y-(-12)=0


Domain of the equation: 3y!=0

y!=0/3

y!=0

y∈R


We add all the numbers together, and all the variables

-5y+2/3y-4=0

We multiply all the terms by the denominator


-5y*3y-4*3y+2=0

Wy multiply elements

-15y^2-12y+2=0

a = -15; b = -12; c = +2;
Δ = b2-4ac
Δ = -122-4·(-15)·2
Δ = 264
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:

$\sqrt{\Delta}=\sqrt{264}=\sqrt{4*66}=\sqrt{4}*\sqrt{66}=2\sqrt{66}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-2\sqrt{66}}{2*-15}=\frac{12-2\sqrt{66}}{-30}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+2\sqrt{66}}{2*-15}=\frac{12+2\sqrt{66}}{-30}
$