x^2-28x=-6x-1

Solution for x^2-28x=-6x-1 equation:

x^2-28x=-6x-1

We move all terms to the left:

x^2-28x-(-6x-1)=0

We get rid of parentheses

x^2-28x+6x+1=0

We add all the numbers together, and all the variables

x^2-22x+1=0

a = 1; b = -22; c = +1;
Δ = b2-4ac
Δ = -222-4·1·1
Δ = 480
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:

$\sqrt{\Delta}=\sqrt{480}=\sqrt{16*30}=\sqrt{16}*\sqrt{30}=4\sqrt{30}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-22)-4\sqrt{30}}{2*1}=\frac{22-4\sqrt{30}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-22)+4\sqrt{30}}{2*1}=\frac{22+4\sqrt{30}}{2}
$