5/3y+7-7=2y-2

Solution for 5/3y+7-7=2y-2 equation:

5/3y+7-7=2y-2

We move all terms to the left:

5/3y+7-7-(2y-2)=0


Domain of the equation: 3y!=0

y!=0/3

y!=0

y∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

5/3y-2y+2=0

We multiply all the terms by the denominator


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

Wy multiply elements

-6y^2+6y+5=0

a = -6; b = 6; c = +5;
Δ = b2-4ac
Δ = 62-4·(-6)·5
Δ = 156
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:

$\sqrt{\Delta}=\sqrt{156}=\sqrt{4*39}=\sqrt{4}*\sqrt{39}=2\sqrt{39}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{39}}{2*-6}=\frac{-6-2\sqrt{39}}{-12}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{39}}{2*-6}=\frac{-6+2\sqrt{39}}{-12}
$