-3(y+9)7y=23

Solution for -3(y+9)7y=23 equation:

-3(y+9)7y=23

We move all terms to the left:

-3(y+9)7y-(23)=0

We multiply parentheses

-21y^2-189y-23=0

a = -21; b = -189; c = -23;
Δ = b2-4ac
Δ = -1892-4·(-21)·(-23)
Δ = 33789
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{-(-189)-\sqrt{33789}}{2*-21}=\frac{189-\sqrt{33789}}{-42}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-189)+\sqrt{33789}}{2*-21}=\frac{189+\sqrt{33789}}{-42}
$