33x^2+55x+55=555

Solution for 33x^2+55x+55=555 equation:

33x^2+55x+55=555

We move all terms to the left:

33x^2+55x+55-(555)=0

We add all the numbers together, and all the variables

33x^2+55x-500=0

a = 33; b = 55; c = -500;
Δ = b2-4ac
Δ = 552-4·33·(-500)
Δ = 69025
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{69025}=\sqrt{25*2761}=\sqrt{25}*\sqrt{2761}=5\sqrt{2761}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(55)-5\sqrt{2761}}{2*33}=\frac{-55-5\sqrt{2761}}{66}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(55)+5\sqrt{2761}}{2*33}=\frac{-55+5\sqrt{2761}}{66}
$