6x+x^2-52=0

Solution for 6x+x^2-52=0 equation:

6x+x^2-52=0

a = 1; b = 6; c = -52;
Δ = b2-4ac
Δ = 62-4·1·(-52)
Δ = 244
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:

$\sqrt{\Delta}=\sqrt{244}=\sqrt{4*61}=\sqrt{4}*\sqrt{61}=2\sqrt{61}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{61}}{2*1}=\frac{-6-2\sqrt{61}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{61}}{2*1}=\frac{-6+2\sqrt{61}}{2}
$