(7/3)(y)=7-3y

Solution for (7/3)(y)=7-3y equation:

(7/3)(y)=7-3y

We move all terms to the left:

(7/3)(y)-(7-3y)=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

(+7/3)y-(-3y+7)=0

We multiply parentheses

7y^2-(-3y+7)=0

We get rid of parentheses

7y^2+3y-7=0

a = 7; b = 3; c = -7;
Δ = b2-4ac
Δ = 32-4·7·(-7)
Δ = 205
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-\sqrt{205}}{2*7}=\frac{-3-\sqrt{205}}{14}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{205}}{2*7}=\frac{-3+\sqrt{205}}{14}
$