3x^2+177=-48x

Solution for 3x^2+177=-48x equation:

3x^2+177=-48x

We move all terms to the left:

3x^2+177-(-48x)=0

We get rid of parentheses

3x^2+48x+177=0

a = 3; b = 48; c = +177;
Δ = b2-4ac
Δ = 482-4·3·177
Δ = 180
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:

$\sqrt{\Delta}=\sqrt{180}=\sqrt{36*5}=\sqrt{36}*\sqrt{5}=6\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(48)-6\sqrt{5}}{2*3}=\frac{-48-6\sqrt{5}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(48)+6\sqrt{5}}{2*3}=\frac{-48+6\sqrt{5}}{6}
$