x+11=x^2/2-13

Solution for x+11=x^2/2-13 equation:

x+11=x^2/2-13

We move all terms to the left:

x+11-(x^2/2-13)=0

We get rid of parentheses

-x^2/2+x+13+11=0

We multiply all the terms by the denominator


-x^2+x*2+13*2+11*2=0

We add all the numbers together, and all the variables

-1x^2+x*2+48=0

Wy multiply elements

-1x^2+2x+48=0

a = -1; b = 2; c = +48;
Δ = b2-4ac
Δ = 22-4·(-1)·48
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-14}{2*-1}=\frac{-16}{-2}
=+8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+14}{2*-1}=\frac{12}{-2}
=-6
$