3(-13+3y)3y=-21

Solution for 3(-13+3y)3y=-21 equation:

3(-13+3y)3y=-21

We move all terms to the left:

3(-13+3y)3y-(-21)=0

We add all the numbers together, and all the variables

3(3y-13)3y-(-21)=0

We add all the numbers together, and all the variables

3(3y-13)3y+21=0

We multiply parentheses

27y^2-117y+21=0

a = 27; b = -117; c = +21;
Δ = b2-4ac
Δ = -1172-4·27·21
Δ = 11421
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:

$\sqrt{\Delta}=\sqrt{11421}=\sqrt{81*141}=\sqrt{81}*\sqrt{141}=9\sqrt{141}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-117)-9\sqrt{141}}{2*27}=\frac{117-9\sqrt{141}}{54}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-117)+9\sqrt{141}}{2*27}=\frac{117+9\sqrt{141}}{54}
$