x2-9x=3x+1

Solution for x2-9x=3x+1 equation:

x2-9x=3x+1

We move all terms to the left:

x2-9x-(3x+1)=0

We add all the numbers together, and all the variables

x^2-9x-(3x+1)=0

We get rid of parentheses

x^2-9x-3x-1=0

We add all the numbers together, and all the variables

x^2-12x-1=0

a = 1; b = -12; c = -1;
Δ = b2-4ac
Δ = -122-4·1·(-1)
Δ = 148
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:

$\sqrt{\Delta}=\sqrt{148}=\sqrt{4*37}=\sqrt{4}*\sqrt{37}=2\sqrt{37}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-2\sqrt{37}}{2*1}=\frac{12-2\sqrt{37}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+2\sqrt{37}}{2*1}=\frac{12+2\sqrt{37}}{2}
$