x^2=(-x+56)

Solution for x^2=(-x+56) equation:

x^2=(-x+56)

We move all terms to the left:

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

We add all the numbers together, and all the variables

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


We calculate terms in parentheses: -((-1x+56)), so:

(-1x+56)

We get rid of parentheses

-1x+56

Back to the equation:

-(-1x+56)


We get rid of parentheses

x^2+1x-56=0

We add all the numbers together, and all the variables

x^2+x-56=0

a = 1; b = 1; c = -56;
Δ = b2-4ac
Δ = 12-4·1·(-56)
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-15}{2*1}=\frac{-16}{2}
=-8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+15}{2*1}=\frac{14}{2}
=7
$