7x=13-x*x

Solution for 7x=13-x*x equation:

7x=13-x*x

We move all terms to the left:

7x-(13-x*x)=0

We add all the numbers together, and all the variables

7x-(-x*x+13)=0

We get rid of parentheses

7x+x*x-13=0

Wy multiply elements

x^2+7x-13=0

a = 1; b = 7; c = -13;
Δ = b2-4ac
Δ = 72-4·1·(-13)
Δ = 101
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{-(7)-\sqrt{101}}{2*1}=\frac{-7-\sqrt{101}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+\sqrt{101}}{2*1}=\frac{-7+\sqrt{101}}{2}
$