68+5x=x2

Solution for 68+5x=x2 equation:

68+5x=x2

We move all terms to the left:

68+5x-(x2)=0

We add all the numbers together, and all the variables

-1x^2+5x+68=0

a = -1; b = 5; c = +68;
Δ = b2-4ac
Δ = 52-4·(-1)·68
Δ = 297
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:

$\sqrt{\Delta}=\sqrt{297}=\sqrt{9*33}=\sqrt{9}*\sqrt{33}=3\sqrt{33}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-3\sqrt{33}}{2*-1}=\frac{-5-3\sqrt{33}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+3\sqrt{33}}{2*-1}=\frac{-5+3\sqrt{33}}{-2}
$