6x^2-8x+1=x+4

Solution for 6x^2-8x+1=x+4 equation:

6x^2-8x+1=x+4

We move all terms to the left:

6x^2-8x+1-(x+4)=0

We get rid of parentheses

6x^2-8x-x-4+1=0

We add all the numbers together, and all the variables

6x^2-9x-3=0

a = 6; b = -9; c = -3;
Δ = b2-4ac
Δ = -92-4·6·(-3)
Δ = 153
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:

$\sqrt{\Delta}=\sqrt{153}=\sqrt{9*17}=\sqrt{9}*\sqrt{17}=3\sqrt{17}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-3\sqrt{17}}{2*6}=\frac{9-3\sqrt{17}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+3\sqrt{17}}{2*6}=\frac{9+3\sqrt{17}}{12}
$