77x=x^2+360

Solution for 77x=x^2+360 equation:

77x=x^2+360

We move all terms to the left:

77x-(x^2+360)=0

We get rid of parentheses

-x^2+77x-360=0

We add all the numbers together, and all the variables

-1x^2+77x-360=0

a = -1; b = 77; c = -360;
Δ = b2-4ac
Δ = 772-4·(-1)·(-360)
Δ = 4489
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4489}=67$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(77)-67}{2*-1}=\frac{-144}{-2}
=+72
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(77)+67}{2*-1}=\frac{-10}{-2}
=+5
$