6x+5=x2

Solution for 6x+5=x2 equation:

6x+5=x2

We move all terms to the left:

6x+5-(x2)=0

We add all the numbers together, and all the variables

-1x^2+6x+5=0

a = -1; b = 6; c = +5;
Δ = b2-4ac
Δ = 62-4·(-1)·5
Δ = 56
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:

$\sqrt{\Delta}=\sqrt{56}=\sqrt{4*14}=\sqrt{4}*\sqrt{14}=2\sqrt{14}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{14}}{2*-1}=\frac{-6-2\sqrt{14}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{14}}{2*-1}=\frac{-6+2\sqrt{14}}{-2}
$