(2/3)y+56=178

Solution for (2/3)y+56=178 equation:

(2/3)y+56=178

We move all terms to the left:

(2/3)y+56-(178)=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+56-178=0

We add all the numbers together, and all the variables

(+2/3)y-122=0

We multiply parentheses

2y^2-122=0

a = 2; b = 0; c = -122;
Δ = b2-4ac
Δ = 02-4·2·(-122)
Δ = 976
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:

$\sqrt{\Delta}=\sqrt{976}=\sqrt{16*61}=\sqrt{16}*\sqrt{61}=4\sqrt{61}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{61}}{2*2}=\frac{0-4\sqrt{61}}{4}
=-\frac{4\sqrt{61}}{4}
=-\sqrt{61}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{61}}{2*2}=\frac{0+4\sqrt{61}}{4}
=\frac{4\sqrt{61}}{4}
=\sqrt{61}
$