(3x^2)+177=255

Solution for (3x^2)+177=255 equation:

(3x^2)+177=255

We move all terms to the left:

(3x^2)+177-(255)=0

We add all the numbers together, and all the variables

3x^2-78=0

a = 3; b = 0; c = -78;
Δ = b2-4ac
Δ = 02-4·3·(-78)
Δ = 936
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:

$\sqrt{\Delta}=\sqrt{936}=\sqrt{36*26}=\sqrt{36}*\sqrt{26}=6\sqrt{26}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{26}}{2*3}=\frac{0-6\sqrt{26}}{6}
=-\frac{6\sqrt{26}}{6}
=-\sqrt{26}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{26}}{2*3}=\frac{0+6\sqrt{26}}{6}
=\frac{6\sqrt{26}}{6}
=\sqrt{26}
$