-31x+56=-x2

Solution for -31x+56=-x2 equation:

-31x+56=-x2

We move all terms to the left:

-31x+56-(-x2)=0

We add all the numbers together, and all the variables

-(-1x^2)-31x+56=0

We get rid of parentheses

1x^2-31x+56=0

We add all the numbers together, and all the variables

x^2-31x+56=0

a = 1; b = -31; c = +56;
Δ = b2-4ac
Δ = -312-4·1·56
Δ = 737
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-31)-\sqrt{737}}{2*1}=\frac{31-\sqrt{737}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-31)+\sqrt{737}}{2*1}=\frac{31+\sqrt{737}}{2}
$