13x-x2=6

Solution for 13x-x2=6 equation:

13x-x2=6

We move all terms to the left:

13x-x2-(6)=0

We add all the numbers together, and all the variables

-1x^2+13x-6=0

a = -1; b = 13; c = -6;
Δ = b2-4ac
Δ = 132-4·(-1)·(-6)
Δ = 145
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(13)-\sqrt{145}}{2*-1}=\frac{-13-\sqrt{145}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+\sqrt{145}}{2*-1}=\frac{-13+\sqrt{145}}{-2}
$