2/3*y+12=32

Solution for 2/3*y+12=32 equation:

2/3*y+12=32

We move all terms to the left:

2/3*y+12-(32)=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

2/3*y-20=0

We multiply all the terms by the denominator


-20*3*y+2=0

Wy multiply elements

-60y*y+2=0

Wy multiply elements

-60y^2+2=0

a = -60; b = 0; c = +2;
Δ = b2-4ac
Δ = 02-4·(-60)·2
Δ = 480
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:

$\sqrt{\Delta}=\sqrt{480}=\sqrt{16*30}=\sqrt{16}*\sqrt{30}=4\sqrt{30}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{30}}{2*-60}=\frac{0-4\sqrt{30}}{-120}
=-\frac{4\sqrt{30}}{-120}
=-\frac{\sqrt{30}}{-30}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{30}}{2*-60}=\frac{0+4\sqrt{30}}{-120}
=\frac{4\sqrt{30}}{-120}
=\frac{\sqrt{30}}{-30}
$