33w+3w^2=w^2+6w+276

Solution for 33w+3w^2=w^2+6w+276 equation:

33w+3w^2=w^2+6w+276

We move all terms to the left:

33w+3w^2-(w^2+6w+276)=0

We get rid of parentheses

3w^2-w^2+33w-6w-276=0

We add all the numbers together, and all the variables

2w^2+27w-276=0

a = 2; b = 27; c = -276;
Δ = b2-4ac
Δ = 272-4·2·(-276)
Δ = 2937
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(27)-\sqrt{2937}}{2*2}=\frac{-27-\sqrt{2937}}{4}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(27)+\sqrt{2937}}{2*2}=\frac{-27+\sqrt{2937}}{4}
$