x^2-13x=30-x

Solution for x^2-13x=30-x equation:

x^2-13x=30-x

We move all terms to the left:

x^2-13x-(30-x)=0

We add all the numbers together, and all the variables

x^2-13x-(-1x+30)=0

We get rid of parentheses

x^2-13x+1x-30=0

We add all the numbers together, and all the variables

x^2-12x-30=0

a = 1; b = -12; c = -30;
Δ = b2-4ac
Δ = -122-4·1·(-30)
Δ = 264
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{264}=\sqrt{4*66}=\sqrt{4}*\sqrt{66}=2\sqrt{66}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-2\sqrt{66}}{2*1}=\frac{12-2\sqrt{66}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+2\sqrt{66}}{2*1}=\frac{12+2\sqrt{66}}{2}
$