51=9x^2+27-30x

Solution for 51=9x^2+27-30x equation:

51=9x^2+27-30x

We move all terms to the left:

51-(9x^2+27-30x)=0

We get rid of parentheses

-9x^2+30x-27+51=0

We add all the numbers together, and all the variables

-9x^2+30x+24=0

a = -9; b = 30; c = +24;
Δ = b2-4ac
Δ = 302-4·(-9)·24
Δ = 1764
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1764}=42$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-42}{2*-9}=\frac{-72}{-18}
=+4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+42}{2*-9}=\frac{12}{-18}
=-2/3
$