9w^2+9w-54=11w+3

Solution for 9w^2+9w-54=11w+3 equation:

9w^2+9w-54=11w+3

We move all terms to the left:

9w^2+9w-54-(11w+3)=0

We get rid of parentheses

9w^2+9w-11w-3-54=0

We add all the numbers together, and all the variables

9w^2-2w-57=0

a = 9; b = -2; c = -57;
Δ = b2-4ac
Δ = -22-4·9·(-57)
Δ = 2056
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{2056}=\sqrt{4*514}=\sqrt{4}*\sqrt{514}=2\sqrt{514}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{514}}{2*9}=\frac{2-2\sqrt{514}}{18}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{514}}{2*9}=\frac{2+2\sqrt{514}}{18}
$