-7(7/3y+6)-2/3y=-15

Solution for -7(7/3y+6)-2/3y=-15 equation:

-7(7/3y+6)-2/3y=-15

We move all terms to the left:

-7(7/3y+6)-2/3y-(-15)=0


Domain of the equation: 3y+6)!=0

y∈R



Domain of the equation: 3y!=0

y!=0/3

y!=0

y∈R


We add all the numbers together, and all the variables

-7(7/3y+6)-2/3y+15=0

We multiply parentheses

-49y-2/3y-42+15=0

We multiply all the terms by the denominator


-49y*3y-42*3y+15*3y-2=0

Wy multiply elements

-147y^2-126y+45y-2=0

We add all the numbers together, and all the variables

-147y^2-81y-2=0

a = -147; b = -81; c = -2;
Δ = b2-4ac
Δ = -812-4·(-147)·(-2)
Δ = 5385
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{-(-81)-\sqrt{5385}}{2*-147}=\frac{81-\sqrt{5385}}{-294}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-81)+\sqrt{5385}}{2*-147}=\frac{81+\sqrt{5385}}{-294}
$