x^2-30=9-2x

Solution for x^2-30=9-2x equation:

x^2-30=9-2x

We move all terms to the left:

x^2-30-(9-2x)=0

We add all the numbers together, and all the variables

x^2-(-2x+9)-30=0

We get rid of parentheses

x^2+2x-9-30=0

We add all the numbers together, and all the variables

x^2+2x-39=0

a = 1; b = 2; c = -39;
Δ = b2-4ac
Δ = 22-4·1·(-39)
Δ = 160
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:

$\sqrt{\Delta}=\sqrt{160}=\sqrt{16*10}=\sqrt{16}*\sqrt{10}=4\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-4\sqrt{10}}{2*1}=\frac{-2-4\sqrt{10}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+4\sqrt{10}}{2*1}=\frac{-2+4\sqrt{10}}{2}
$