4x-2+6x=x2

Solution for 4x-2+6x=x2 equation:

4x-2+6x=x2

We move all terms to the left:

4x-2+6x-(x2)=0

We add all the numbers together, and all the variables

-1x^2+10x-2=0

a = -1; b = 10; c = -2;
Δ = b2-4ac
Δ = 102-4·(-1)·(-2)
Δ = 92
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:

$\sqrt{\Delta}=\sqrt{92}=\sqrt{4*23}=\sqrt{4}*\sqrt{23}=2\sqrt{23}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{23}}{2*-1}=\frac{-10-2\sqrt{23}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{23}}{2*-1}=\frac{-10+2\sqrt{23}}{-2}
$